Match summary
The dominant Edinburgh side powered eight ahead of their Glasgow rivals at the summit of the Scottish top flight to strengthen their early title credentials and deepen the malaise around Brendan Rodgers' side.
Alexandros Kyziridis' fine strike and Lawrence Shankland's penalty gave Derek McInnes' side a two-goal advantage that the title holders could not recover from.
The young defender - one of three youngsters in the Celtic starting lineup - scored an own goal in the early stages to put Hearts ahead at a bouncing their home ground, and it was the 22-year-old's foul that led to the spot-kick.
A stylish finish from McGregor of the season had swiftly equalized Hearts' opener, and the Swedish attacker almost put Celtic in front, choosing placement over power and allowing the Hearts keeper to save from close range.
But the unstoppable Hearts side regained dominance to hand Celtic to successive league defeats for the first time since 2023.
It also gives the Edinburgh side a commanding advantage at the top of the table.
The last time they were this far ahead was in the 2005-2006 season under their former manager, when they ended as runners-up - one of just four occasions that a team has not secured the title having held such a lead in the last three decades.
McInnes, whose former team were second to Celtic on four occasions, has been at pains to play down championship discussions, as Hearts seek their maiden league title since 1960.
Rodgers has seen it all before at Celtic - both perfect and shaky beginnings to a season. He's yet to finish second best.
But on the weekend's performance, this Hearts team showed they need to be taken seriously.
Hearts started with the self-assurance of a side unbeaten in the league this season - fans' favourite Kyziridis poked a cross in for the striker to stab wide.
The Glasgow team didn't help themselves with some unusual sloppiness in possession and they faltered under their initial test.
Claudio Braga's header was tipped onto the woodwork by Kasper Schmeichel and Shankland's return ball was turned into the net by the unfortunate Murray, in for the injured Cameron Carter-Vickers.
The away side found their rhythm and started building moves. From a flowing attack, the midfielder released the full-back to set up McGregor, who slotted home.
Apart from the Nygren chance, the visitors found it hard to generate chances for striker Kenny or his replacement Shin Yamada amid the absence of injured forwards Kelechi Iheanacho and Daizen Maeda.
The home team regained their intensity and versatility in creating chances in the opposition half. Kyziridis, a standout performer of the club's scouting network, fired a low shot past Schmeichel from the just outside the area.
Almost straight away, the defender tripped the midfielder in the right side of the box and the penalty taker scored. 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 somewhat summed up in a couple of moments involving record signing Arne Engles.
The set-piece from Engles delivery was in stark contrast to his European display in the continental victory over their Austrian opponents and the Belgium international was then booked for a professional foul.
The Hearts manager: "You see how hard the players work, the team spirit. That's not always enough to win games week in, week out.
"What we have got, is good technical ability. You're seeing that from multiple individuals who have been here previously. Some of the new signings are eager to show that.
"We're in a positive moment at the minute, but it's only three points. It's important for us to maintain this form. We've got much work ahead, loads to do. After the first two rounds is typically a benchmark of your standing."
Celtic manager Brendan Rodgers: "The second goal was disappointing from our perspective. We failed to push up when the play was recycled as a defensive unit so when they pass the ball, they should have players offside but didn't. We have got to improve with the attempt.
"There's still so many points to play for. It's only the beginning. It's just nine matches. Obviously, being eight adrift is not what we would want. The comfort is there's so many games to play.
"We now have to focus on the present and look to find more consistency and more quality in our play."
The Glasgow club are returning to their stadium on midweek against promoted side Falkirk (19:45 GMT). At the identical hour in the Scottish Premiership, Hearts are at their opponents' ground.
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