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At a glance
The dominant Edinburgh side surged eight points clear of Celtic at the top of the Scottish top flight to bolster their early-season championship claims and worsen the malaise around Brendan Rodgers' side.
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.
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 spot-kick.
A stylish finish from McGregor of the season had quickly cancelled out the first goal, and Benjamin Nygren almost put Rodgers' team in front, opting for finesse over power and allowing Alexander Schwolow to save from close range.
But Derek McInnes' irrepressible Hearts seized control again to hand Celtic to back-to-back losses for the initial occasion since 2023.
It also gives the Edinburgh side a commanding advantage at the summit.
The last time they were so far clear was in the 2005-2006 season under George Burley, when they ultimately finished second - one of just four occasions that a team has not secured the title after building such an advantage in the last three decades.
McInnes, whose Aberdeen side were runners-up to the champions on four occasions, has been at pains to play down championship discussions, as Hearts seek their maiden league title since the 1960s.
The Celtic boss has experienced this previously at Celtic - both flawless and stuttering starts to a season. He's yet to finish second best.
But on Sunday's evidence, this Edinburgh outfit showed they need to be taken seriously.
Hearts started with the self-assurance of a side undefeated in the league this season - fans' favourite Kyziridis poked a cross in for the striker to fire off target.
The Glasgow team didn't aid their cause with some uncharacteristic carelessness in possession and they buckled under their first real examination.
A headed effort from Braga was touched on to a post by the Celtic keeper and the follow-up from Shankland was turned into the net by the hapless defender, in for the injured Cameron Carter-Vickers.
Celtic found their rhythm and started stringing passes together. From one such move, Sebastian Tounekti released the full-back to set up the captain, who rolled in.
Aside from the Nygren chance, Celtic found it hard to generate chances for striker Kenny or his substitute Yamada amid the unavailability of stricken attackers their key strikers.
The home team rediscovered their energy and versatility in attacking from across the final third. The Greek forward, one of the finds of the club's relationship with shareholder Tony Bloom's Jamestown Analytics, fired a low shot past Schmeichel from the edge of the box.
Immediately after, the defender fouled Braga in the right side of the box and Shankland converted. And it could've been an even more handsome win, had substitute Ageu not been denied by Schmeichel.
Celtic's second half was somewhat summed up in two incidents involving big-money recruit Engles.
The set-piece from Engles delivery was in stark contrast to his European display in the continental victory over Sturm Graz and the Belgium international was then booked for a cynical foul.
The Hearts manager: "The effort from the squad is evident, the togetherness. That's not always enough to win games consistently.
"Our strength lies in, is skillful players. You're witnessing it from multiple individuals 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 loads to do, loads to do. Following the initial fixtures is normally an indication of your standing."
The Celtic boss: "The second goal was disappointing from our perspective. We didn't move when the ball went back as a defensive unit so when they play it, they should have players offside but didn't. We have got to do better with the shot.
"There's still so many points 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 so many games to play.
"Our attention must turn on the present and look to find more consistency and more quality in our play."
Celtic are returning to their stadium on Wednesday against promoted side Falkirk (evening kick-off). At the same time in the Scottish Premiership, Hearts are at St Mirren.
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