Seconds after Stephen Elliott's second-minute header appeared to cross the line before being blocked by Celtic midfielder Joe Ledley, Hoops skipper Scott Brown drove low past Jambos goalkeeper Jamie MacDonald for the opener.
Goals from midfielder Victor Wanyama and Ledley had the points secured by the interval before striker Gary Hooper concluded the romp on the hour with a typical poacher's goal from close range.
Neil Lennon's men extended their domestic winning run to 16 games to remain on course for the treble and on this form, they will take some stopping.
Ahead of what again turned out to be a controversial fixture, Lennon made one change, winger James Forrest replacing Kris Commons - who started on the bench along with new signing, striker Pawel Brozek.
Jambos boss Paulo Sergio made three changes with Danny Grainger, Mehdi Taouil and Andrew Driver coming in for injured David Templeton, suspended Ian Black and Rudi Skacel - who was named among the substitutes.
Hearts, facing the prospect of a winding up order next week if a tax bill is not paid to HMRC, had been the last team in Scotland to beat the Hoops, last October and who know what might have happened if they had got the first big decision of the game in their favour.
In the second minute Driver's corner from the right found Andy Webster at the back post and his header back across goal was met a couple of yards out by Elliott.
The Jambos' striker seemed certain to score but his header was blocked by Ledley, although television pictures suggested the ball was over the line before it was scrambled away by Parkhead keeper Fraser Forster.
However, there was no whistle from referee Willie Collum, or flag from assistant Andy Tait, to signal a goal.
Celtic raced up the park and when the ball broke to Brown, following a cross from James Forrest, he slammed the ball past MacDonald from 12 yards for his fourth goal in four games.
There was around 30 seconds between the two incidents and with Tynecastle in uproar Brown drove over the bar as the SPL leaders threatened again.
From then on it was all too easy for Celtic.
With Team GB coach Stuart Pearce watching from the main stand, there was more woe for Hearts in the 20th minute when they failed to clear properly a Charlie Mulgrew corner from the left.
Forrest returned the ball into the box and it broke for Wanyama who fired high past the helpless MacDonald.
The Gorgie men all but unravelled thereafter and in the 31st minute, after skipper Marius Zaliukas had conceded possession to Brown, they found themselves three down.
With the Jambos defence all over the place, Hooper fed Georgios Samaras down the left and he skipped easily past Ryan McGowan before crossing for Ledley to head into an empty net.
Mulgrew was booked seconds before the interval for diving in the box but it was little consolation for the home fans.
Gary Glen replaced Driver at the start of the second half but a recovery looked a tall order for the Edinburgh side.
Hearts were bullish and determined but continued to make unforced errors which drew cries of frustration from their fans, who might have sensed, rightly, that number four was on its way.
On the hour, Hooper set up Ledley and his low drive hit the far post and rebounded off Grainger for a corner.
Mulgrew fired the ball over and when Wanyama headed it back in the centre Hooper pounced to knock the ball over the line from barely a yard out.
The points were tagged, bagged and ready to go back to Glasgow.
Defender Daniel Majstorovic replaced Thomas Rogne, Anthony Stokes came on for Hooper and Poland striker Brozek made his debut in the 73rd minute when he took over from Brown.
In the 80th minute MacDonald made a good diving save from Samaras' powerful long-range drive and this time Hearts defended the corner comfortably.
However, by then it was a matter of Celtic playing out time until the final whistle ended the Jambos' misery.