Match summary
Rampant Hearts powered eight ahead of their Glasgow rivals at the top of the Scottish top flight to strengthen their early title credentials and deepen the struggles around Brendan Rodgers' side.
Alexandros Kyziridis' fine strike and Lawrence Shankland's penalty gave the Hearts team a 3-1 lead that the title holders could not overcome.
The young defender - one of three youngsters in the Celtic XI - slashed into his own net in the early stages to put the home side ahead at a bouncing their home ground, and it was the youngster's infringement that led to the penalty.
A stylish finish from McGregor of the season had swiftly equalized the first goal, and the Swedish attacker almost put Celtic in front, opting for finesse over power and allowing Alexander Schwolow to make a crucial stop.
But Derek McInnes' irrepressible Hearts seized control again to consign the visitors to successive league defeats for the initial occasion since last year.
It also gives the Edinburgh side a significant lead at the top of the table.
The last time they were so far clear was in 2005-06 under their former manager, when they ended as runners-up - a rare instance that a team has not secured the title having held such a lead in the last three decades.
The Hearts coach, whose former team were runners-up to the champions on multiple times, has been at pains to play down championship discussions, as the club seek their first top-flight crown since the 1960s.
The Celtic boss has experienced this previously at Celtic - both flawless and stuttering starts to a season. He's never ended as runner-up.
But on the weekend's performance, this Hearts team showed they deserve serious consideration.
Hearts started with the confidence of a side unbeaten in the league this season - fans' favourite Kyziridis poked a cross in for Shankland to fire off target.
Celtic didn't help themselves with some unusual sloppiness in possession and they buckled under their first real examination.
Claudio Braga's header was touched on to a post by Kasper Schmeichel and Shankland's return ball was diverted goalwards by the hapless defender, in for the injured Cameron Carter-Vickers.
Celtic grew into the contest and started stringing passes together. From a flowing attack, Sebastian Tounekti released Tierney to square for the captain, who slotted home.
Apart from the opportunity for Nygren, the visitors struggled to create much for striker Kenny or his replacement Shin Yamada amid the absence of stricken attackers their key strikers.
Hearts regained their intensity and versatility in creating chances in the opposition half. Kyziridis, one of the finds of the club's scouting network, fired a low shot past the goalkeeper from the edge of the box.
Immediately after, Murray tripped Braga in the inside right channel and Shankland converted. And it could've been an even more handsome win, had substitute Ageu not been stopped by the shot-stopper.
Celtic's second half was partially encapsulated in a couple of moments involving record signing Arne Engles.
The set-piece from Engles delivery was in sharp opposition to his European display in the continental victory over their Austrian opponents and the Belgium international was then yellow-carded for a professional foul.
The Hearts manager: "The effort from the squad is evident, the togetherness. That's not sufficient on its own to win games week in, week out.
"Our strength lies in, is skillful players. You're seeing that from a lot of players who have been here before. Recent additions are keen to demonstrate their quality.
"We're in a positive moment at the minute, but it's just one win. It's important for us to maintain this form. We've got loads to do, loads to do. Following the initial fixtures is typically a benchmark of your standing."
Celtic manager Brendan Rodgers: "It's a really poor goal from our perspective. We failed to push up when the ball went back as a line so when they play it, they should have players offside but didn't. We have got to improve with the attempt.
"Plenty of matches to play for. It's still so early. It's just nine matches. Clearly, being eight points behind is not what we would want. The comfort is there's numerous fixtures to play.
"We now have to focus on the here and now and look to achieve greater stability and better performance in our play."
The Glasgow club are returning to their stadium on midweek against newly-promoted Falkirk (19:45 GMT). At the identical hour in the Scottish Premiership, Hearts are at their opponents' ground.
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