Fabricio Coloccini was sent off for a dangerous challenge on Suarez late on.
While Liverpool have now gone five league games without a defeat - their longest unbeaten run in 2012 - it was a game in which the familiar story of their season unfolded as they failed to make the most of their possession and chances.
The visitors displayed defensive fortitude to frustrate their hosts, but Suarez's goal denied the Magpies a first win at Anfield in 18 league games since April 1994.
Skipper Steven Gerrard was playing his 600th game for the Reds - moving him to 10th in the club's list of all-time appearance makers - and the midfielder has been the inspiration for his team on a regular basis since his debut in November 1998.
Coloccini red 'laughable' - Owen
"Not having that at all. [Coloccini] didn't touch him and to say there was intent is laughable. Let me tell you, he kicks a moving ball a thousand times a day and doesn't miss it once. If he wanted to connect with a standing leg then he wouldn't have missed. He pulls out at the last minute and doesn't touch him. Not having that's a red at all."
But it was Suarez who was Newcastle's chief tormentor in a game the Reds began with obvious urgency.
The home side did not take long to get into their passing stride and they quickly started to pile on the pressure, with winger Raheem Sterling's pace and trickery a particular concern for the visitors.
Suarez is never far from the action and he was soon left indignant when referee Anthony Taylor ignored his penalty appeal after he was caught by Coloccini.
Newcastle had to show the steel that has been a hallmark of their game this season to keep the Reds at arm's length.
The closest Liverpool came to a goal in the first half was when Suarez had an angled shot across goal saved by the foot of keeper Tim Krul and a Suso strike was deflected over.
Yohan Cabaye's goal was the first scored by a Newcastle player at Anfield in the league since Patrick Kluivert in 2004 (excludes last season's own goal by Daniel Agger).
Liverpool have only won three of their last 15 Premier League matches at Anfield (W3 D6 L6)
Liverpool (23) had more than twice as many efforts on goal as Newcastle (11)
But the visitors gradually came into the game and then stunned the home side by taking the lead.
Hatem Ben Arfa jinked to the byline and crossed to the far post where Cabaye controlled before rifling home a shot.
It was a goal that highlighted exactly the type of ruthlessness in front of goal Liverpool sorely miss.
Suarez had a low curling shot saved and Nuri Sahin scuffed an effort narrowly wide as it seemed Liverpool's problems in front of goal would continue.
But, after Jonas Gutierrez gave the ball away, Suarez brilliantly took down a long Enrique pass before touching the ball around Krul and slotting into an empty net.
Newcastle boss Alan Pardew "surprised" by Coloccini red card
The Uruguayan then set up Jonjo Shelvey and Sterling for chances to win the game but both wasted their opportunities.
Shelvey failed to get the required purchase on a pull-back, while Sterling was denied when his shot was deflected high off the sliding Steven Taylor.
As Liverpool pressed for a late goal, Newcastle almost exposed the home side at the back with Papiss Cisse volleying wide and Ben Arfa having a shot saved by keeper Brad Jones.
Coloccini's 84th-minute dismissal put the visitors under some late pressure and a deflected Suarez free-kick looped over before both teams had to settle for a draw.
47:06 Inswinging corner taken by Jesus Fernandez Saez, clearance by Demba Ba.
45:01 The referee gets the second half underway.
45:00+2:07 The players leave the pitch at half time.
45:00+1:45 Steven Taylor has an effort at goal from the edge of the box that misses to the right of the target.
45:00+1:10 Handball decision goes against Jesus Fernandez Saez. The free kick is swung in right-footed by Yohan Cabaye, Steven Gerrard
makes a clearance.
44:50 Luis Suarez produces a right-footed shot from long range which goes wide right of the target.
44:11 Effort from outside the area by Yohan Cabaye goes wide right of the goal.
42:53 The assist for the goal came from Hatem Ben Arfa.
42:53 GOAL - Yohan Cabaye:Liverpool 0 - 1 Newcastle A goal is scored by Yohan Cabaye from inside the box to the top right corner of the goal. Liverpool 0-1 Newcastle.
42:46 The ball is swung over by Hatem Ben Arfa,
40:52 Outswinging corner taken right-footed by Steven Gerrard, Demba Ba makes a clearance. Effort on goal by Jesus Fernandez Saez
from just outside the penalty area goes harmlessly over the target.
40:31 Jesus Fernandez Saez takes a shot. Blocked by Fabricio Coloccini.
39:56 The ball is swung over by Luis Suarez.
38:43 Free kick awarded for an unfair challenge on Raheem Sterling by Yohan Cabaye. Strike on goal comes in from Steven Gerrard
from the free kick.
35:18 Centre by Danny Simpson, clearance made by Daniel Agger.
31:32 Hatem Ben Arfa fouled by Jesus Fernandez Saez, the ref awards a free kick. Davide Santon takes the free kick.
31:17 Short corner taken by Nuri Sahin.
31:06 Steven Gerrard crosses the ball, clearance made by Fabricio Coloccini.
30:53 Daniel Agger delivers the ball, Davide Santon makes a clearance.
29:18 Foul by Joe Allen on Demba Ba, free kick awarded. Free kick crossed right-footed by Yohan Cabaye from left channel. The official
flags Steven Taylor offside. Indirect free kick taken by Brad Jones.
27:56 Headed effort from inside the area by Luis Suarez misses to the left of the goal.
27:33 The ball is sent over by Sanchez Jose Enrique, clearance by Steven Taylor.
25:57 Substitution James Perch goes off and Danny Simpson comes on.
24:55 Unfair challenge on Jonas Gutierrez by Nuri Sahin results in a free kick. Direct free kick taken by Tim Krul.
21:37 Corner taken left-footed by Nuri Sahin from the right by-line to the near post, clearance by Demba Ba.
21:28 Daniel Agger fouled by Demba Ba, the ref awards a free kick. Joe Allen takes the direct free kick.
21:16 Luis Suarez concedes a free kick for a foul on Davide Santon. Tim Krul takes the free kick.
20:51 Luis Suarez takes a shot. Save made by Tim Krul.
19:57 Hatem Ben Arfa has a shot and went wide right of the goal.
18:12 Free kick awarded for an unfair challenge on Luis Suarez by James Perch. Luis Suarez has an effort direct from the free kick.
16:28 The ball is crossed by Vurnon Anita, Steven Gerrard makes a clearance.
16:12 The ball is delivered by Jonas Gutierrez.
15:03 Nuri Sahin concedes a free kick for a foul on James Perch. Fabricio Coloccini restarts play with the free kick.
14:03 Effort on goal by Demba Ba from long range goes harmlessly over the bar.
10:46 Foul by Fabricio Coloccini on Luis Suarez, free kick awarded. Steven Gerrard restarts play with the free kick.
10:07 Shot from outside the area by Raheem Sterling misses to the left of the target.
7:49 Inswinging corner taken by Nuri Sahin from the right by-line, clearance made by Demba Ba.
7:20 Inswinging corner taken by Steven Gerrard from the left by-line, save made by Tim Krul.
7:09 Jesus Fernandez Saez takes a shot. Blocked by Davide Santon.
5:45 The ball is crossed by Andre Wisdom.
4:17 Raheem Sterling delivers the ball, Davide Santon manages to make a clearance.
3:13 Short corner taken by Raheem Sterling.
2:55 Centre by Raheem Sterling, Fabricio Coloccini manages to make a clearance.
1:30 Steven Gerrard takes a shot. Steven Taylor gets a block in. Vurnon Anita gives away a free kick for an unfair challenge on
Raheem Sterling. Steven Gerrard delivers the ball from the free kick right-footed from left wing, save by Tim Krul.
0:00 The match gets underway.
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