Match ends, Celtic 3, Heart of Midlothian 0.
Celtic eased into the last eight of the League Cup with victory over Hearts, who were made to pay for poor defending and wasting a couple of golden chances.
John Guidetti thrashed in the opening goal on 24 minutes during a period of Celtic dominance.
Either side of half-time, Jamie Walker hit the crossbar for Hearts and Osman Sow missed the target with a penalty.
Kris Commons then converted from the spot and Adam Eckersley knocked in an own goal from an Anthony Stokes cross.
Manager Ronny Deila chose a strong side for a tournament Celtic have not won since 2009, with Commons returning along with skipper Scott Brown, Craig Gordon and Stefan Johansen.
Stokes drilled an early shot narrowly wide for the hosts but it was Hearts, flying high at the top of the Championship, who settled into the more assured rhythm.
The visitors won three corners in quick succession, with only a lunging interception from Jason Denayer denying Sow a tap-in from Callum Paterson's low delivery.
Hearts defender Alim Ozturk then made a terrible mess of shielding the ball in his own penalty area, expecting Neil Alexander to gather and leaving Guidetti with just the goalkeeper to beat but the Swede swiped wide of the target.
Suddenly it was Celtic who were in the ascendancy and Paterson needed to block a Stokes effort, Denayer scuffed a shot into Alexander's arms and Commons also had a low shot saved.
Alexander did well to push away a thunderous 18-yard strike from Brown but the 36-year-old was soon beaten.
Emilio Izaguirre delivered a great, deep cross from the left and Hearts skipper Danny Wilson could only divert the ball into the path of Guidetti, who thumped the ball home from 10 yards via the post for his first goal since joining on loan from Manchester City.
Guidetti almost had a second goal when he diverted a low shot from Callum McGregor. Alexander was deceived but Eckersley was on the line to clear.
With Celtic now in control, another excellent Izaguirre delivery flashed across goal to cannon off the shins of Morgaro Gomis and it needed an instinctive save from Alexander to prevent an own goal.
Hearts were presented with a fantastic opportunity on the stroke of half time as an errant pass from Stokes allowed Walker to race in behind the Celtic defence. The midfielder cracked a shot beyond Gordon from the edge of the penalty area only to see it hammer back off the crossbar.
An even better chance came the Edinburgh side's way early in the second half when referee Willie Collum pointed to the spot as Sow toppled under pressure from Virgil van Dijk.
Sow's fall appeared to owe more to his own clumsiness but the striker could not profit from the gift and blazed an appalling penalty high over the crossbar.
Just moments later, Commons showed Sow how to score from 12 yards, lashing the ball low into the corner following Ozturk's overly robust shoulder charge on Guidetti.
And the game slipped beyond Hearts' reach on the hour when Eckersley chose to use his chest to cushion a Stokes cross and inadvertently steered the ball into his own net from six yards.
Alexander needed to save close-range efforts from Stokes and Izaguirre, who was a menace down the left flank all evening.
The Honduras full-back cut into the penalty area with 10 minutes remaining but his shot from a tight angle did not match his earlier good work.
Aleksandar Tonev had earlier touched in a shot from fellow substitute Stefan Scepovic from an offside position but could not make amends as his late shot fizzed just wide.
Celtic manager Ronny Deila: "I'm very pleased, I think we're going in the right direction all the time now.
"What I'm most pleased about is two things. One we worked as a team, eleven players who wanted to win the ball and work together.
"And two we are started to create something on the sides.
"I think it's important to keep consistency in the team because if you change too much as I've done twice then we haven't played well and I can understand why."
Hearts head coach Robbie Neilson: "I thought the game hinged on the penalty.
"We went 1-0 down but still stayed strong. We miss the penalty and the game totally changed from there, they go up the park and get a penalty and it's very difficult when the crowd starts getting behind them, the atmosphere changes and they start getting confidence.
"I'm pleased with the performance overall. Disappointed with the result - at the end of the day the league's the main thing for us and gear up now for Sunday."
- 22DenayerBooked at 4minsSubstituted forO'Connellat 46'minutesBooked at 86mins
- 5van Dijk
- 42McGregorSubstituted forTonevat 72'minutes
- 9GuidettiSubstituted forScepovicat 64'minutes
- 5OzturkBooked at 56mins
- 7WalkerSubstituted forKeatingsat 78'minutes
- 18CarrickSubstituted forHoltat 64'minutes
- 20SowSubstituted forEl Hassnaouiat 78'minutesBooked at 86mins
- 9El Hassnaoui
- William Collum
- Shots on Target
Second Half ends, Celtic 3, Heart of Midlothian 0.
Corner, Heart of Midlothian. Conceded by Efe Ambrose.
Foul by Scott Brown (Celtic).
Prince Buaben (Heart of Midlothian) wins a free kick in the attacking half.
Attempt missed. Aleksandar Tonev (Celtic) left footed shot from outside the box misses to the left.
Attempt blocked. Anthony Stokes (Celtic) right footed shot from long range on the left is blocked.
Attempt blocked. Soufian El Hassnaoui (Heart of Midlothian) right footed shot from outside the box is blocked.
Soufian El Hassnaoui (Heart of Midlothian) is shown the yellow card.
Emilio Izaguirre (Celtic) wins a free kick in the attacking half.
Foul by Soufian El Hassnaoui (Heart of Midlothian).
Eoghan O'Connell (Celtic) is shown the yellow card.
Foul by Eoghan O'Connell (Celtic).
James Keatings (Heart of Midlothian) wins a free kick in the defensive half.
Hand ball by Soufian El Hassnaoui (Heart of Midlothian).
Substitution, Heart of Midlothian. James Keatings replaces Jamie Walker.
Substitution, Heart of Midlothian. Soufian El Hassnaoui replaces Osman Sow.
Corner, Heart of Midlothian. Conceded by Stefan Johansen.
Foul by Anthony Stokes (Celtic).
Callum Paterson (Heart of Midlothian) wins a free kick on the left wing.