Key points
Rampant Hearts powered eight points clear of Celtic at the summit of the Scottish top flight to strengthen their early title credentials and worsen the struggles around the Celtic team.
Alexandros Kyziridis' fine strike and a spot-kick from Shankland gave the Hearts team a 3-1 lead that the reigning champions could not overcome.
Dane Murray - one of three youngsters in the Celtic XI - 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 penalty.
A stylish finish from McGregor of the season had swiftly equalized Hearts' opener, and the Swedish attacker almost put Rodgers' team in front, opting for finesse over power and allowing the Hearts keeper to save from close range.
But the unstoppable Hearts side regained dominance to hand the visitors to back-to-back losses for the initial occasion since 2023.
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.
McInnes, whose former team were runners-up to the champions on four occasions, has been at pains to downplay title talk, as Hearts seek their first top-flight crown since 1960.
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 Sunday's evidence, this Hearts team showed they deserve serious consideration.
Hearts started with the self-assurance of a side unbeaten in the league this season - fans' favourite Kyziridis delivered a ball for Shankland to fire off target.
Celtic didn't aid their cause with some unusual sloppiness in possession and they faltered 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 found their rhythm and started building moves. From one such move, 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 lone frontman Jonny Kenny or his substitute Yamada amid the unavailability of stricken attackers their key strikers.
The home team rediscovered their energy and versatility in creating chances in the opposition half. The Greek forward, one of the finds of the club's relationship with shareholder Tony Bloom's Jamestown Analytics, fired a low shot past the goalkeeper from the just outside the area.
Immediately after, the defender fouled Braga in the right side of the box and the penalty taker scored. And it could've been an more comprehensive victory, had replacement Ageu not been stopped by the shot-stopper.
Celtic's second half was somewhat summed up in two incidents 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 national team player was then booked for a professional foul.
The Hearts manager: "The effort from the squad is evident, the togetherness. That's not always enough to win games week in, week out.
"Our strength lies in, is good technical ability. You're seeing that from a lot of players who have been here before. Recent additions are keen to demonstrate their quality.
"We've got a good thing going 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 normally an indication of your standing."
Celtic manager Brendan Rodgers: "The second goal was disappointing from our perspective. We failed to push up when the ball went back as a line so when they pass the ball, they should have players offside but weren'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 numerous fixtures to play.
"Our attention must turn on the present 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 same time in the Scottish Premiership, the Edinburgh outfit are at St Mirren.
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