Hearts were left Petroved as Celtic advanced to the last eight of the Scottish Cup.
Bulgarian midfield ace Stilian Petrov struck two superb first-half goals to kill off the Edinburgh side who finished the contest with just nine players.
Paul Hartley and Alan Maybury were both sent off in the final minutes of a meaty encounter – both for picking up two yellow cards.
Henrik Larsson piled on the misery for Hearts deep into injury-time when he headed in the third goal after a Petrov shot had been parried by Craig Gordon.
Now Petrov is convinced Celtic can go on and win the trophy: "It was a great team performance and the important thing was to win," he said.
"It's easy to score when you have such great players around you like Henrik Larsson and Chris Sutton and everyone in the team deserves credit.
"I've never scored a hat-trick in my life and I came close but I'm just happy we're in the next round.
"If we continue to play this way, then we can go on and win the cup." Martin O'Neill echoed: "This is a hard place to come, but the players were terrific. The first half is as good as we have played recently and we've turned in some good performances.
"Stilian's hit a rich vein of form just now and he's getting into the right positions. His contribution is very positive and he's getting help from all over the pitch." It was a tie Celtic dominated from start to finish against a disappointing Hearts side which failed to come up to scratch.
John Hartson, involved in an ugly elbowing incident with Andy Webster the last time the teams met last month, did not feature due to a niggling back injury.
It meant Sutton starting up front with Larsson and, with Bobo Balde also absent due to African Cup of Nations duty, there was a place in the defence for Scotland Under-21 cap John Kennedy.
Mark de Vries and Phil Stamp both recovered from stomach bugs to take their places in the Hearts' line-up.
Celtic made their intentions clear from the start and, within a minute, Petrov tried an ambitious volley from just outside the area which sailed well over the top.
But it did not take the midfielder long to find his range. Just three minutes had elapsed when Sutton headed the ball on for Larsson who, in turn, threaded the ball into Petrov's path.
The Bulgarian kept his cool to side-foot the ball past an exposed Gordon for the opening goal.
Celtic were clearly up for it and chased and harried Hearts all afternoon and did not give them time to dwell on the ball.
Larsson forced an early mistake from Steven Pressley, but Webster came to Hearts' rescue to cut out the Swede's intended pass for Sutton.
Hearts rallied briefly and Kennedy did well to hook a low cross from Dennis Wyness away with de Vries hovering menacingly.
But it took a fantastic save from Gordon to keep Celtic to just one goal after 12 minutes. Maybury put his defence in trouble with a foolish pass in front of Pressley which Larsson siezed on.
He laid the ball back for Sutton but Gordon stood up well to palm the shot over the crossbar for a corner.
From Alan Thompson's kick, Sutton was left unguarded at the near post but he send his header into the sidenetting from a difficult angle.
Celtic had a firm grip on the midfield and Hearts were second to very ball in that area with Neil Lennon getting through a power of work.
Sutton was just inches away from getting his head to a Thompson corner at the back post after Kennedy had flicked the ball on as Hearts had another narrow escape midway through the half.
Hearts had only one serious attempt at goal in the first half and, even then, Rab Douglas was not over-extended.
Wyness put Hartley in the clear but the midfielder could only poke the ball tamely at Douglas when he had the time and space to be more troublesome.
But there was no way back for Hearts after 32 minutes when Petrov nabbed his second goal after a wonderful move with the same three players involved.
Sutton fed Larsson who flicked the ball into the path of Petrov, who did not have to break his stride as he crashed a shot high into the net past Gordon.
Tempers flared minutes later as Hearts' frustrations spilled over with Stamp, Lennon and Harley all going into referee Young's notebook. Hartley was lucky not to get a straight red card as he went in for a loose ball with Lennon with his elbow.
Stamp tried to get a goal back three minutes from the break from a rehearsed free-kick but he pulled his shot well wide of target.
Hearts changed things early in the second half with Kevin McKenna and Robbie Neilson replacing Robert Sloan and Neil MacFarlane as Craig Levein tried to turn the tide.
But it was Celtic who continued to hold the upper hand. Larsson was just short of connecting with a cut-back from Sutton on the edge of the six-yard box after another flowing Celtic move.
Maybury became the fourth player to be booked when he hauled down Kennedy after 56 minutes.
There was a glimmer of hope for Hearts when de Vries wriggled clear of Kennedy but his low shot was just inches wide of Douglas's left-hand post.
But their efforts on goal were few and far between and even the introduction of Andy Kirk for Patrick Kisnorbo late on failed to have any impact.
The task became impossible when Hartley made a rash challenge on Lennon to earn his second booking and an automatic red card.
Petrov had a great chance for his hat-trick with just a minute left when he was all alone in the Hearts' area but hoisted his shot well wide of goal.
Then, in injury-time, Maybury was also given his marching orders after a late challenge on Lennon.
Hearts rubbed salt into the wound when Larsson added a third after Gordon had done well to get down to a shot from Petrov.
Hearts manager Levein had no complaints about either sending off: "Both were fair enough. You have to compete with Celtic as they are a big physical side." Man of the Match: Stilian Petrov – two sweetly-taken goals and tormented Hearts with his running throughout the 90 minutes.