Match summary
Rampant Hearts surged eight ahead of their Glasgow rivals at the summit of the Scottish top flight to strengthen their early championship claims and deepen the struggles around Brendan Rodgers' side.
A superb goal from Kyziridis and a spot-kick from Shankland 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 - slashed into his own net early on to put Hearts ahead at a bouncing Tynecastle, and it was the youngster's infringement that led to the spot-kick.
Callum McGregor's classy first goal of the season had quickly cancelled out the first goal, and Benjamin Nygren almost put Celtic in front, opting for finesse over power and allowing Alexander Schwolow to save from close range.
But the unstoppable Hearts side regained dominance to hand the visitors to back-to-back losses for the first time since 2023.
It also gives the Hearts a significant lead at the top of the table.
The previous occasion they were this far ahead was in 2005-06 under George Burley, when they ultimately finished second - a rare instance that a team has failed to win the title after building such an advantage in the last three decades.
The Hearts coach, whose former team were runners-up to the champions on multiple times, has been at pains to downplay title talk, as the club seek their first top-flight crown since the 1960s.
Rodgers has seen it all before at Celtic - both perfect and shaky beginnings 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 confidence of a side unbeaten in the league this season - fans' favourite Kyziridis delivered a ball for Shankland to stab wide.
The Glasgow team didn't aid their cause with some uncharacteristic carelessness in possession and they faltered under their initial test.
A headed effort from Braga was touched on to a post by the Celtic keeper and Shankland's return ball was turned into the net by the hapless defender, in for the injured Cameron Carter-Vickers.
Celtic found their rhythm and started building moves. From a flowing attack, Sebastian Tounekti released Tierney to square for McGregor, who slotted home.
Apart from the opportunity for Nygren, the visitors struggled to create much for striker Kenny or his replacement Shin Yamada amid the unavailability of injured forwards their key strikers.
Hearts regained their intensity and adaptability in attacking from across the final third. The Greek forward, a standout performer of the club's scouting network, struck low past Schmeichel from the edge of the box.
Immediately after, Murray fouled Braga in the right side of the box and the penalty taker scored. And it could've been an even more handsome win, had substitute Ageu not been denied by the shot-stopper.
Celtic's second half was somewhat summed up in a couple of moments involving big-money recruit Engles.
The midfielder's wayward free-kick delivery was in sharp opposition to his midweek exploits in the Europa League win over Sturm Graz and the national team player was then booked for a professional foul.
The Hearts manager: "You see how hard the players work, the togetherness. That's not always enough to win games week in, week out.
"Our strength lies in, is skillful players. You're witnessing it 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 just one win. It's crucial 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: "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 ought to be caught offside but weren't. We have got to improve with the shot.
"Plenty of matches to play for. It's still so early. It's only nine games in. Obviously, being eight adrift is not ideal. The positive is there's so many games to play.
"Our attention must turn on the present and look to find more consistency and better performance in our play."
Celtic are back at home on midweek against newly-promoted Falkirk (evening kick-off). At the same time in the Scottish Premiership, Hearts are at St Mirren.
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