Match summary
The dominant Edinburgh side powered eight ahead of Celtic at the summit of the Scottish Premiership to strengthen their early-season championship claims 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 reigning champions could not recover from.
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 energetic their home ground, and it was the 22-year-old's foul that led to the penalty.
Callum McGregor's classy first goal of the season had swiftly equalized Hearts' opener, and the Swedish attacker almost put Rodgers' team in front, choosing placement over power and allowing Alexander Schwolow to save from close range.
But Derek McInnes' irrepressible Hearts regained dominance to consign the visitors to successive league defeats for the first time since 2023.
It also gives the Hearts a commanding advantage at the summit.
The last time they were this far ahead was in the 2005-2006 season under their former manager, when they ultimately finished second - a rare instance that a team has failed to win the title having held such a lead in the last three decades.
McInnes, whose Aberdeen side were runners-up to the champions on multiple times, has been working hard to play down title talk, as Hearts seek their maiden league title since the 1960s.
Rodgers has experienced this previously at Celtic - both perfect and shaky beginnings to a season. He's yet to finish second best.
But on the weekend's performance, this Edinburgh outfit showed they need to be taken seriously.
The Edinburgh side started with the self-assurance of a side undefeated in the league this season - the popular attacker delivered a ball for Shankland to fire off target.
The Glasgow team didn't help themselves with some uncharacteristic carelessness in possession and they faltered under their initial test.
A headed effort from Braga was tipped onto the woodwork by the Celtic keeper and the follow-up from Shankland was diverted goalwards by the unfortunate Murray, in for the absent center-back.
Celtic found their rhythm and started building moves. From one such move, Sebastian Tounekti released Tierney to square for the captain, who slotted home.
Aside from the opportunity for Nygren, the visitors found it hard to generate chances for striker Kenny or his replacement Shin Yamada amid the unavailability of injured forwards Kelechi Iheanacho and Daizen Maeda.
The home team rediscovered their energy and adaptability in attacking from across the final third. Kyziridis, one of the finds of the club's scouting network, fired a low shot past Schmeichel from the edge of the box.
Immediately after, the defender tripped Braga in the inside right channel and the penalty taker scored. And it could've been an more comprehensive victory, had substitute Ageu not been denied by Schmeichel.
The visitors' performance after the break was partially encapsulated in a couple of moments involving big-money recruit Engles.
The midfielder's wayward free-kick delivery was in stark contrast to his European display in the continental victory over Sturm Graz and the national team player was then booked for a professional foul.
The Hearts manager: "The effort from the squad is evident, the team spirit. That's not always enough to win games consistently.
"What we have got, is good technical ability. You're witnessing it from multiple individuals who have been here before. Recent additions are eager to show that.
"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 much work ahead, plenty to improve. Following the initial fixtures is typically a benchmark of where you are."
Celtic manager Brendan Rodgers: "The second goal was disappointing from our perspective. We didn't move when the play was recycled as a defensive unit so when they play it, they ought to be caught offside but weren't. We have got to do better with the attempt.
"There's still so many points to play for. It's still so early. It's just nine matches. Clearly, being eight adrift is not ideal. The comfort is there's numerous fixtures to play.
"Our attention must turn 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 top division, the Edinburgh outfit are at St Mirren.
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