The defending champions' appalling record at Arsenal - they had not beaten the Gunners at the Emirates Stadium or Highbury in the league for more than 37 years - did not offer Roberto Mancini's men much encouragement of managing that before kick-off.
But Koscielny's 10th-minute sending off, after he had wrestled Dzeko to the ground inside the area by wrapping two arms around the Bosnian striker to prevent him running on to a Gareth Barry header, handed City the perfect platform to change that awful statistic, and keep their neighbours in sight.
City's long wait to beat Arsenal
Manchester City had waited more than 37 years for an away league win against Arsenal. None of their last 27 league visits to Highbury or Emirates Stadium ended in victory, with their previous success coming when Asa Hartford, Joe Royle and Rodney Marsh scored in a 3-2 win at Highbury on 4 October, 1975.
Dzeko made a hash of the resulting penalty, firing it straight at Wojciech Szczesny's legs and seeing the Gunners keeper grab the ball after it rolled back towards him along the goalline.
It did not take City long to make their extra man count, however. Arsenal switched off at a free-kick, which Barry took quickly, and Carlos Tevez slid Milner clear to beat Szczesny with a powerful angled finish.
More chances followed, with Javi Garcia heading the best of them wide. Arsenal could do little but try to halt the relentless pressure, but they conceded a second goal after 32 minutes.
Again, more could have been done more to prevent it. Milner fired in a dangerous cross after Pablo Zabaleta got the better of Kieran Gibbs down the right and, although Szczesny kept out Tevez's initial effort, Dzeko was on hand to tap home the rebound.
Only a Wilshere header off the line stopped Garcia heading home a third before half-time and, at the interval, City might have been thinking of how they could give their goal-difference a boost.
Wenger surprised by Koscielny red card
Instead, Arsenal showed commendable spirit to stop the flood of City attacks, even if they rarely threatened at the other end.
Szczesny did well to dive at the feet of Tevez when he ran clear but, aside from an Olivier Giroud header that flew over Hart's bar, that was the most meaningful incident of any kind until Kompany saw red.
City's captain got the ball when he slid in on Wilshere and protested his innocence to referee Dean, but the official made it clear he felt it was a dangerous challenge.
With parity restored in terms of men on the field, the home fans tried to roar their side forward.
But the closest Arsenal came to a reply was when substitute Lescott denied Walcott, leaving Arsene Wenger's men six points adrift of a top-four spot, albeit with a game in hand on fourth-placed Tottenham.
Arsenal manager Arsene Wenger:
" "It was frustrating [to go down to 10 men] but we got away with it [with the penalty miss].
"We were down to 10 men with 80 minutes to go and knew it would be a difficult game. "We gave away two cheap goals, at 10 men you keep it 0-0 and you never know.
"But we were too timid and did not have enough authority on the game. We let them dictate the game to us and when we went 1-0 down it was difficult."
Manchester City manager Roberto Mancini:
"If you play with 10 players it is very difficult [like Arsenal had to do for most of the game].
"But, we started with a good attitude and pressed high as we wanted to win the game, it was easier after the sending off. Second half we were too soft and I thought the game could re-open.
"It was an important victory. We knew it was difficult to play here [at Emirates Stadium]."
95:28 The final whistle goes and the game is over.
90:00+3:33 Free kick awarded for a foul by Aleksandar Kolarov on Aaron Ramsey. Free kick taken by Bacary Sagna.
90:00+2:30 Short corner taken by James Milner from the right by-line.
90:00+2:06 Substitution David Silva goes off and Aleksandar Kolarov comes on.
90:00+1:35 The ball is crossed by Kieran Gibbs, Olivier Giroud has a volleyed shot. Save by Joe Hart.
89:53 Theo Walcott takes a shot. Joleon Lescott makes a clearance.
89:03 Handball by Mario Balotelli. Free kick taken by Wojciech Szczesny.
87:49 Substitution Mario Balotelli is brought on as a substitute for Edin Dzeko.
87:05 Inswinging corner taken right-footed by Theo Walcott from the left by-line, save by Joe Hart.
86:03 Santi Cazorla crosses the ball from the free kick right-footed from right channel.
86:03 Booking Gareth Barry booked for unsporting behaviour.
85:57 Gareth Barry concedes a free kick for a foul on Jack Wilshere.
85:42 The ball is delivered by Bacary Sagna, Joleon Lescott manages to make a clearance.
83:23 Aaron Ramsey delivers the ball, clearance by Gael Clichy.
82:25 Free kick awarded for an unfair challenge on Jack Wilshere by David Silva. Free kick crossed left-footed by Jack Wilshere,
Edin Dzeko manages to make a clearance.
81:39 Kieran Gibbs sends in a cross, Gael Clichy manages to make a clearance.
80:43 Theo Walcott is adjudged to have handled the ball. Matija Nastasic restarts play with the free kick.
80:18 James Milner produces a left-footed shot from the edge of the area and misses to the left of the goal.
77:33 Free kick awarded for a foul by Olivier Giroud on Francisco Javi Garcia. Joleon Lescott takes the free kick.
76:35 Gareth Barry restarts play with the free kick.
76:35 Substitution Joleon Lescott joins the action as a substitute, replacing Carlos Tevez.
76:35 Theo Walcott concedes a free kick for a foul on James Milner.
76:18 Shot by Carlos Tevez. Kieran Gibbs gets a block in.
75:32 Santi Cazorla delivers the ball from the free kick right-footed from left channel, clearance by Matija Nastasic.
75:32 Booking Booking for Francisco Javi Garcia for unsporting behaviour.
74:49 Sent off Vincent Kompany receives a red card for serious foul play.
74:30 Vincent Kompany concedes a free kick for a foul on Jack Wilshere.
71:16 The ball is crossed by Santi Cazorla, Close range header by Olivier Giroud goes over the crossbar.
71:16 Booking The referee cautions Gael Clichy for unsporting behaviour.
71:05 Gael Clichy concedes a free kick for a foul on Bacary Sagna.
68:56 Francisco Javi Garcia challenges Olivier Giroud unfairly and gives away a free kick. Thomas Vermaelen takes the direct free
68:01 Free kick awarded for a foul by Edin Dzeko on Bacary Sagna. Free kick taken by Wojciech Szczesny.
67:01 David Silva delivers the ball in from the corner, blocked by Jack Wilshere.
66:33 Olivier Giroud concedes a free kick for a foul on Vincent Kompany. Vincent Kompany takes the free kick.
65:32 Effort on goal by Santi Cazorla from just inside the penalty area goes over the target.
64:47 Theo Walcott fouled by Matija Nastasic, the ref awards a free kick. Jack Wilshere delivers the ball from the free kick left-footed
from right channel.
Correction - 63:48 Joe Hart takes the free kick.
63:48 Vincent Kompany takes the direct free kick.
63:48 Booking Jack Wilshere booked for unsporting behaviour.
Correction - 62:59 Theo Walcott gives away a free kick for an unfair challenge on Vincent Kompany.
62:59 Free kick awarded for a foul by Theo Walcott on Vincent Kompany.
62:34 Edin Dzeko takes a shot. Per Mertesacker gets a block in.
62:23 Centre by David Silva, clearance made by Thomas Vermaelen.
61:33 The ball is swung over by Carlos Tevez, save by Wojciech Szczesny.
60:48 Substitution Aaron Ramsey comes on in place of Vassiriki Diaby.
59:46 Unfair challenge on Jack Wilshere by Edin Dzeko results in a free kick. Jack Wilshere takes the direct free kick.
58:13 Bacary Sagna delivers the ball.
56:49 Substitution Olivier Giroud joins the action as a substitute, replacing Lukas Podolski.
55:42 Jack Wilshere gives away a free kick for an unfair challenge on Francisco Javi Garcia. Carlos Tevez takes the direct free
54:47 Wojciech Szczesny restarts play with the free kick.
54:47 Booking Booking for James Milner for unsporting behaviour.
54:39 Free kick awarded for a foul by James Milner on Jack Wilshere.
53:50 Free kick awarded for a foul by Bacary Sagna on Gareth Barry. David Silva takes the free kick.
52:38 Free kick awarded for a foul by Edin Dzeko on Thomas Vermaelen. Thomas Vermaelen takes the free kick.
51:14 The ball is crossed by Bacary Sagna, Kieran Gibbs takes a shot. Francisco Javi Garcia gets a block in.
50:48 David Silva challenges Jack Wilshere unfairly and gives away a free kick. Free kick taken by Jack Wilshere.
49:59 Free kick awarded for a foul by Jack Wilshere on David Silva. Free kick taken by Joe Hart.
49:23 Theo Walcott fouled by Matija Nastasic, the ref awards a free kick. Free kick crossed by Jack Wilshere, clearance made by
48:50 James Milner produces a cross, Edin Dzeko has a headed effort at goal from deep inside the area missing to the left of the
47:19 Theo Walcott is flagged offside by the assistant referee. Free kick taken by Matija Nastasic.
46:31 The offside flag is raised against Pablo Zabaleta. Wojciech Szczesny takes the free kick.
45:31 The official flags Theo Walcott offside. Joe Hart takes the indirect free kick.
45:01 The second half has started.
45:00+2:59 The first half comes to an end.
45:00+0:46 Direct free kick taken by Francisco Javi Garcia.
45:00+0:46 Booking The referee shows Thomas Vermaelen a yellow card.
45:00+0:36 Foul by Thomas Vermaelen on Edin Dzeko, free kick awarded.
42:58 Outswinging corner taken by James Milner from the right by-line, Francisco Javi Garcia takes a shot. Clearance made by Jack
41:31 Vassiriki Diaby has an effort at goal from deep inside the area missing to the right of the goal.
40:03 Unfair challenge on Jack Wilshere by David Silva results in a free kick. Jack Wilshere crosses the ball from the free kick
left-footed from right channel, Pablo Zabaleta manages to make a clearance.
39:26 The ball is delivered by Lukas Podolski, clearance by Gael Clichy.
37:50 The assistant referee signals for offside against James Milner. Kieran Gibbs restarts play with the free kick.
36:52 The assistant referee signals for offside against Theo Walcott. Indirect free kick taken by Matija Nastasic.
34:26 Lukas Podolski takes a shot. Save made by Joe Hart.
33:36 Pablo Zabaleta gives away a free kick for an unfair challenge on Lukas Podolski. Free kick taken by Kieran Gibbs.
32:56 Thomas Vermaelen fouled by Carlos Tevez, the ref awards a free kick. Direct free kick taken by Wojciech Szczesny.
Correction - 31:03 James Milner crosses the ball, Carlos Tevez takes a shot. Save by Wojciech Szczesny.
31:03 James Milner delivers the ball, Carlos Tevez takes a shot. Wojciech Szczesny makes a save.
Correction - 31:02 The assist for the goal came from Carlos Tevez.
Correction - 31:02 GOAL - Edin Dzeko:Arsenal 0 - 2 Man City Edin Dzeko finds the back of the net with a goal from inside the six-yard box to the bottom left corner of the goal. Arsenal
0-2 Man City.
31:02 Assist on the goal came from Carlos Tevez.
31:02 GOAL - Edin Dzeko:Arsenal 0 - 2 Man City Edin Dzeko finds the net with a goal from close range to the bottom left corner of the goal. Arsenal 0-2 Man City.
29:55 The ball is sent over by Santi Cazorla, save made by Joe Hart.
27:17 Lukas Podolski fouled by Vincent Kompany, the ref awards a free kick. Direct strike on goal from the free kick comes in from
26:42 Gareth Barry delivers the ball, Headed effort from deep inside the area by Francisco Javi Garcia misses to the left of the
26:23 Short corner taken by David Silva.
26:06 Effort on goal by David Silva from 20 yards. Bacary Sagna gets a block in.
25:10 The ball is sent over by David Silva, Shot by Carlos Tevez. Save made by Wojciech Szczesny.
23:38 Effort from outside the penalty box by James Milner goes wide left of the target.
20:49 Assist on the goal came from Carlos Tevez.
20:49 GOAL - James Milner:Arsenal 0 - 1 Man City James Milner finds the net with a goal from inside the penalty box to the top left corner of the goal. Arsenal 0-1 Man City.
20:31 Free kick awarded for a foul by Lukas Podolski on Francisco Javi Garcia. Gareth Barry restarts play with the free kick.
19:36 Edin Dzeko has an effort at goal from deep inside the area missing to the left of the target.
16:40 Effort on goal by Theo Walcott from just inside the area clears the bar.
16:03 Corner taken by Jack Wilshere, save made by Joe Hart.
14:53 The ball is delivered by James Milner, Headed effort from deep inside the area by Vincent Kompany misses to the left of the
14:30 James Milner decides to take the corner short.
13:08 Foul by James Milner on Lukas Podolski, free kick awarded. Free kick taken by Wojciech Szczesny.
11:53 Substitution Per Mertesacker is brought on as a substitute for Alex Oxlade-Chamberlain.
10:15 A fantastic save by Wojciech Szczesny from penalty by Edin Dzeko. Arsenal 0-0 Man City.
9:13 Sent off Laurent Koscielny sent from the field by the ref for professional foul.
8:34 Unfair challenge on Edin Dzeko by Laurent Koscielny results in a Penalty.
7:55 Outswinging corner taken by David Silva, Pablo Zabaleta takes a shot. Bacary Sagna gets a block in.
7:31 David Silva takes a shot. Thomas Vermaelen gets a block in.
4:32 Lukas Podolski concedes a free kick for a foul on James Milner. Free kick taken by Joe Hart.
3:53 The ball is delivered by Bacary Sagna, Matija Nastasic makes a clearance.
1:54 David Silva takes the outswinging corner, Lukas Podolski manages to make a clearance.
0:00 The match begins.
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