Pre-match talk was of the third-placed Gorgie side challenging the Old Firm for the title but they never recovered after falling behind to a James Forrest goal in the seventh minute.
The Hoops created numerous chances in a powerful performance and a second-half double from Anthony Stokes and a goal from substitute Paddy McCourt, on for the injured Forrest in the first half, cemented Celtic's place at the top of the SPL while at the same time ending Jambo hopes.
It was as convincing a performance as the Celtic fans have seen from their side this season as the hosts' defensive problems were forgotten.
Charlie Mulgrew was asked to team up with Thomas Rogne for the visit of the in-form Edinburgh side.
Rogne was the only recognised centre-back available to boss Neil Lennon and Mulgrew, normally a left-back, replaced Daniel Majstorovic who injured a hamstring against Aberdeen on Saturday.
Lennon made two other changes as Forrest, back from suspension, and midfielder Joe Ledley replaced Niall McGinn and McCourt, who both dropped to the bench.
Hearts, the last team to beat Celtic when they triumphed 2-0 at Tynecastle in November, arrived in Glasgow unbeaten in 11 SPL games.
During that run they had climbed to within two points of second-placed Rangers and seven behind the Hoops, having played a game less than the home side.
Their ability to exploit any potential weakness at the heart of the Celtic rearguard, however, was dealt a blow when powerful striker Kevin Kyle failed to recover from his groin injury and missed the game.
The visitors, though, had barely ventured up the park when Celtic took the lead in the seventh minute through the returning Forrest.
A clever flick by striker Gary Hooper was picked up by skipper Scott Brown who drove forward before releasing the Hoops winger on the left side of the penalty area and he appeared to take Hearts goalkeeper Marian Kello by surprise when he lashed in an unstoppable shot from 16 yards.
As Celtic dominated proceedings half-chances were being created -and spurned - with some regularity.
Unfortunately for Forrest, he had to depart in the 24th minute after picking up an injury, but ragged Hearts' task did not look any easier with the appearance of the talented McCourt.
Hearts' first real attempt came moments later in a rare break when striker Stephen Elliott flashed an angled shot from 14 yards past the far post.
Celtic refused to relinquish control of a match that was becoming increasingly tetchy by the minute, the home fans irked by the somewhat erratic performance of referee Euan Norris.
However, there was a moment of danger for Lennon's side in the 37th minute Hearts left-back Lee Wallace made a surging run in to the Parkhead box after taking a Rudi Skacel pass but his driven cross found no takers.
Moments later hesitation by Stokes in the Hearts box cost Celtic another chance to double their lead.
In the final frantic moments of the first half, as the visitors wobbled again, Ledley fired just wide from the edge of the box.
The SPL leaders should have had the points safely in the bag by the interval but with only one goal in it, Hearts retained hope.
Within a minute of the restart Kello was forced to make a point-blank save from Hooper after the former Scunthorpe hitman had again raced clear of the square defence.
The Tynecastle side, though, were punished again in the 50th minute when Stokes struck with a wonderful free-kick to give the home side some breathing space.
Celtic left-back Emilio Izaguirre was pulled back outside the Hearts box by Ismael Bouzid and from the resultant set-piece, the former Hibernian striker calmly curled the ball over the wall and past the diving Kello.
A huge melee ensued soon after when Black went in on McCourt, who had originally been fouled by Eggert Jonsson, and when order was restored Black and Hearts skipper Marius Zaliukas, and Brown and Stokes, were handed yellow cards by Norris who was taking fearsome stick from the home crowd.
Moments later, with the visitors all over the place, Hooper shot over the bar from close range.
The evening got worse for the wayward visitors. In the 71st minute Hooper again raced clear on to a Beram Kayal pass only to be brought down by Kello when he tried to round the goalkeeper, leaving the supporting Stokes to tap into an open goal for his second.
Celtic were rampant and in the 80th minute, with the Hearts defence again all at sea, McCourt curled in goal number four from just inside the box.
It was a fine way to end the Jambos' unbeaten league run while handing out a warning to chasing Old Firm rivals Rangers.