The Hoops responded to their shock 1-0 home defeat by Inverness 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.
Striker Gary Hooper grabbed 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 forced their way in front in the 10th minute when Kris Commons' cross from the left found Lassad who confidently volleyed it low past Jamie MacDonald at his near post.
However, five minutes later, when Joe Ledley fouled Jamie Walker 25 yards from goal, the home side should have levelled when Ryan Stevenson flighted the free-kick on to the head of striker Callum Paterson but he missed his header completely and the ball flew wide.
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 Kevin McHattie's 25-yard free-kick.
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 Kelvin Wilson fouled Stevenson inside the box but Forster completed another great display by diving low to his right to thwart Zaliukas.