The Hoops have stuttered in their journey to the top of the SPL this season but they responded to their shock home 1-0 defeat by Inverness at the weekend in fine style with goals from striker Lassad Nouioui and right-back Mikael Lustig before Charlie Mulgrew's cut-back was deflected into his own net by Gorgie midfielder Ryan Stevenson.
The second half was a formality for the clinical Parkhead side with striker Gary Hooper grabbing a fourth late in the game before Hoops goalkeeper Fraser Forster showed why he has forced his way into the England set-up by saving a late penalty from Hearts skipper Marius Zaliukas.
Celtic's impressive performance must have put a smile on the face of manager Neil Lennon who had rather dramatically threatened to quit the club following an altercation with fans during the Caley defeat, and he took the acclaim of the travelling supporters as his side coasted to victory.
The future of financially-stricken Hearts is still far from secure but they had their moments in this game, only to be foiled, in the main, by Forster.
Lennon made three changes to his side with defender Kelvin Wilson, midfielder Joe Ledley and Lassad in for Adam Matthews, Georgios Samaras and Tony Watt, who all started on the bench, while Kevin McHattie replaced injured Jambos left-back Danny Grainger
It was a typically frantic and frenetic start to one of the best SPL fixtures but by the interval the points were on their way back to Glasgow.
In the fourth minute Hooper set up Kris Commons whose shot from 12 yards, dispatched almost casually, was beaten away by Jamie MacDonald.
The home side responded by forcing a couple of corners and there was an appeal for a penalty when the ball looked like it might have struck Lassad on the arm following Jamie Walker's delivery, but referee Willie Collum waved play on.
Celtic forced their way in front in the 10th minute when Commons' cross from the left, after he had taken a pass from Beram Kayal, found Lassad who confidently volleyed it low past MacDonald at his near post.
However, five minutes later, when Ledley fouled Walker 25 yards from goal, the home side should have levelled when Stevenson flighted the free-kick on to the head of striker Callum Paterson but he missed his header completely and the ball flew wide.
Moments later, there was another Jambos penalty claim when Celtic's stand-in skipper Wilson, previously warned by Collum after a couple of hefty challenges, clashed with Paterson but again the official stood firm
Midway through the first half, however, Celtic showed their ruthless side when Lustig put them two ahead.
The Sweden international started the move on the right and when Lassad's cut back broke to him 12 yards out after Commons had been foiled by Darren Barr in a packed Hearts penalty area, he stabbed the ball past MacDonald from around seven yards.
Three minutes later a remarkable save from Forster prevented the home side getting back into the game.
After the big Geordie had parried Stevenson's powerful free-kick from 30 yards it looked like Zaliukas must score but somehow Forster clawed away his close-range header and the danger was averted when Hearts midfielder Ryan McGowan hit the side-netting.
The home side slumped further behind on the half-hour mark when Commons' deep cross from the right ended up at the far side of the box with Mulgrew whose cut-back was put past his own keeper by the hapless Stevenson in trying to block.
The game was effectively over at the interval although Hearts started the second half in determined mood and four minutes after the restart Forster pulled off another fine diving save, this time from McHattie's 25-yard free-kick.
But Celtic were in command.
Commons then fired over the bar from the edge of the box before a low drive by Lassad from a similar distance produced a save by MacDonald.
John McGlynn's men continued to battle away in their search for a lifeline and in the 71st minute Forster made a decent save from Mehdi Taouil, who had replaced Jason Holt.
The visitors, though, remained dangerous and in the 82nd minute, after MacDonald had made a save from Commons, they stretched their lead further when Hooper volleyed in a Mulgrew cross from six yards.
With two minutes remaining Hearts were awarded a penalty when Wilson fouled Stevenson inside the box but Forster completed another great display by diving low to his right to thwart Zaliukas.