At a glance
The dominant Edinburgh side surged eight ahead of Celtic at the top of the Scottish top flight to bolster their early-season title credentials and deepen the struggles around Brendan Rodgers' side.
Alexandros Kyziridis' fine strike and Lawrence Shankland's penalty gave the Hearts team a two-goal advantage that the title holders could not recover from.
The young defender - among three youth players in the Celtic XI - scored an own goal early on to put the home side ahead at a bouncing their home ground, and it was the 22-year-old's foul that led to the spot-kick.
Callum McGregor's classy first goal of the season had swiftly equalized the first goal, and Benjamin Nygren almost put Rodgers' team in front, opting for finesse over power and allowing Alexander Schwolow to make a crucial stop.
But the unstoppable Hearts side seized control again to hand the visitors to successive league defeats 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 this far ahead was in the 2005-2006 season under George Burley, when they ended as runners-up - 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 former team were second to Celtic on four occasions, has been at pains to play down title talk, as the club seek their first top-flight crown since the 1960s.
The Celtic boss has seen it all before at Celtic - both flawless and stuttering starts to a season. He's never ended as runner-up.
But on Sunday's evidence, this Edinburgh outfit showed they need to be taken seriously.
Hearts started with the self-assurance of a side unbeaten in the league this season - the popular attacker delivered a ball for Shankland to stab wide.
Celtic didn't help themselves with some uncharacteristic carelessness in possession and they faltered under their first real examination.
A headed effort from Braga was tipped onto the woodwork 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 grew into the contest and started stringing passes together. From one such move, Sebastian Tounekti released the full-back to square for McGregor, who slotted home.
Aside from the opportunity for Nygren, Celtic found it hard to generate chances for lone frontman Jonny Kenny or his substitute Yamada amid the absence of stricken attackers their key strikers.
The home team rediscovered their energy and adaptability in creating chances in the opposition half. Kyziridis, a standout performer of the club's relationship with shareholder Tony Bloom's Jamestown Analytics, struck low past Schmeichel from the edge of the box.
Almost straight away, the defender fouled Braga in the right side of the box and the penalty taker converted. And it could've been an more comprehensive victory, had replacement Ageu not been denied by Schmeichel.
Celtic's second half was partially encapsulated in a couple of moments involving big-money recruit Engles.
The set-piece from Engles delivery was in stark contrast to his European display in the Europa League win 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 togetherness. That's not sufficient on its own 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. Recent additions are eager to show that.
"We're in a positive moment at the minute, but it's only three points. It's crucial for us to keep winning. We've got loads to do, plenty to improve. Following the initial fixtures is typically a benchmark of where you are."
The Celtic boss: "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 do better with the shot.
"There's still so many points to play for. It's still so early. It's only nine games in. Clearly, being eight points behind is not ideal. The positive is there's numerous fixtures to play.
"We now have to focus on the present and look to achieve greater stability and more quality in our play."
The Glasgow club are back at home on midweek against promoted side Falkirk (evening kick-off). At the same time in the top division, the Edinburgh outfit are at St Mirren.
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