Midfielder Olivier Ntcham opened the scoring for the home side on the half-hour mark with a drive, with second-half goals from defender Christopher Jullien, midfielder Callum McGregor, substitute Ryan Christie and defender Jozo Simunovic completing the rout.
Parkhead cheered loudly when news of Killie's second goal in their 2-1 win over second-placed Rangers came through, with Steven Gerrard's side now 10 points behind the champions, albeit with a game in hand.
Daniel Stendel had promised to attack the home side in his first appearance at Celtic Park as Jambos boss and, while his side put in a decent first-half performance, they left battered and bruised and still bottom of the table.
Celtic revealed a strength in depth that no one in Scottish football can match.
Neil Lennon brought back Fraser Forster, Greg Taylor, Simunovic, McGregor and attacking duo Odsonne Edouard and Leigh Griffiths after resting them in the William Hill Scottish Cup win against Clyde on Sunday.
Hearts defender John Souttar passed a fitness test on an ankle injury to return along with Jamie Walker and Anthony McDonald and the visitors survived a couple of early scares.
Griffiths combined with Edouard in the 12th minute before rifling a powerful shot just over the bar.
Then Tynecastle goalkeeper Joel Periera made a double save, first from James Forrest, the second from Griffiths.
McDonald did not look too pleased to be replaced by Conor Washington in the 29th minute but no one in maroon was happy moments later when Ntcham smartly returned the ball into the net after Pereira had punched an Edouard drive straight to his feet.
The goalkeeper could have done better but Hearts, to their credit, kept pushing forward and finished the half strongly.
Sean Clare made way for Langer for the start of the second half and he had been on the pitch less than a minute when Jullien climbed at the back post to head in Griffiths' corner from the left.
Following yet another corner minutes later, Simunovic and Brown hit woodwork before a swift Celtic break saw McGregor swap passes with Taylor and the midfielder fired through the legs of Souttar and into the net.
Hearts staggered through the rest of the game.
Pereira flew to his left to parry a Forrest volley from the edge of the box, while at the other end Forster got a fingertip on a 25-yard drive from Walker.
Christie came on for Griffiths in the 65th minute and two minutes later he took a pass from the tireless Taylor and his shot from 12 yards came off Gorgie defender Craig Halkett and beat Pereira.
With 10 minutes remaining and the Jambos on their knees, Simunovic then headed in a Christie corner from six yards for number five, with Langer letting his frustration getting the better of him in the 86th minute when he lunged at Brown.