Match summary
Rampant Hearts powered eight ahead of their Glasgow rivals at the summit of the Scottish Premiership to bolster their early-season championship claims and worsen the struggles around Brendan Rodgers' side.
A superb goal from Kyziridis and Lawrence Shankland's penalty gave Derek McInnes' side a two-goal advantage that the reigning champions could not overcome.
Dane Murray - among three youth players in the Celtic XI - scored an own goal in the early stages to put Hearts ahead at a bouncing Tynecastle, and it was the youngster's infringement 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, opting for finesse over power and allowing the Hearts keeper to make a crucial stop.
But Derek McInnes' irrepressible Hearts seized control again to hand Celtic to successive league defeats for the first time since last year.
It also gives the Hearts a commanding advantage at the summit.
The last time they were this far ahead was in 2005-06 under their former manager, when they ultimately finished second - one of just four occasions 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 four occasions, has been working hard to downplay championship discussions, as Hearts seek their first top-flight crown since the 1960s.
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 the weekend's performance, this Hearts team showed they need to be taken seriously.
Hearts started with the confidence of a side unbeaten in the league this season - the popular attacker poked a cross in for the striker to stab wide.
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 opportunity for Nygren, Celtic struggled to create much for lone frontman Jonny Kenny or his substitute Yamada amid the unavailability of injured forwards Kelechi Iheanacho and Daizen Maeda.
Hearts regained their intensity and adaptability in attacking from across the final third. The Greek forward, one of the finds of the club's scouting network, fired a low shot past Schmeichel from the just outside the area.
Immediately after, Murray tripped Braga in the right side of the box and the penalty taker converted. And it could've been an even more handsome win, had substitute Ageu not been stopped by Schmeichel.
The visitors' performance after the break 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 yellow-carded for a cynical foul.
The Hearts manager: "You see how hard the players work, the togetherness. That's not always enough to win games consistently.
"What we have got, is skillful players. You're witnessing it 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 loads to do, loads to do. Following the initial fixtures is typically a benchmark of your standing."
Celtic manager Brendan Rodgers: "The second goal was disappointing from our perspective. We didn't move when the ball went back as a defensive unit so when they pass the ball, they ought to be caught offside but didn't. We have got to do better 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 what we would want. The positive is there's so many games to play.
"We now have to focus on the present and look to find more consistency and better performance in our play."
The Glasgow club are returning to their stadium on midweek against newly-promoted Falkirk (evening kick-off). At the identical hour in the top division, Hearts are at St Mirren.
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