Key points
Rampant Hearts powered eight ahead of their Glasgow rivals at the top of the Scottish top flight to bolster their early title credentials and worsen the struggles around Brendan Rodgers' side.
A superb goal from Kyziridis and Lawrence Shankland's penalty gave the Hearts team a two-goal advantage that the title holders could not overcome.
Dane Murray - among three youth players in the Celtic XI - scored an own goal in the early stages 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 quickly cancelled out the first goal, and the Swedish attacker almost put Celtic in front, choosing placement over power and allowing Alexander Schwolow to make a crucial stop.
But Derek McInnes' irrepressible Hearts regained dominance 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 top of the table.
The last time they were so far clear was in the 2005-2006 season under George Burley, when they ultimately finished second - a rare instance that a team has not secured the title after building such an advantage in the past 27 years.
The Hearts coach, whose Aberdeen side were second to Celtic on multiple times, has been working hard to play down championship discussions, as Hearts seek their first top-flight crown since 1960.
The Celtic boss has seen it all before at the club - 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 deserve serious consideration.
Hearts started with the self-assurance of a side undefeated in the league this season - the popular attacker 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 Shankland's return ball was diverted goalwards by the unfortunate Murray, in for the absent center-back.
Celtic found their rhythm and started building moves. From a flowing attack, Sebastian Tounekti released Tierney to set up the captain, who rolled in.
Aside from the opportunity for Nygren, Celtic found it hard to generate chances for striker Kenny or his replacement Shin Yamada amid the absence of stricken attackers their key strikers.
Hearts regained their intensity and adaptability in attacking from across the final third. Kyziridis, 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 edge of the box.
Almost straight away, Murray fouled the midfielder in the inside right channel and the penalty taker converted. 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 two incidents 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 Sturm Graz and the Belgium international was then yellow-carded for a cynical foul.
Hearts head coach Derek McInnes: "You see how hard the players work, 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 only three points. It's important for us to keep winning. We've got much work ahead, plenty to improve. After the first two rounds is normally an indication of where you are."
The Celtic boss: "It's a really poor goal from our perspective. We didn't move when the play was recycled as a line so when they play it, they should have players offside but didn't. We have got to improve with the attempt.
"Plenty of matches to play for. It's still so early. It's only nine games in. Clearly, being eight points behind is not ideal. The comfort is there's numerous fixtures to play.
"We now have to focus on the present and look to find more consistency and better performance in our play."
Celtic are returning to their stadium on Wednesday against newly-promoted Falkirk (19:45 GMT). At the same time in the top division, Hearts are at their opponents' ground.
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