Key points
Rampant Hearts powered eight points clear of their Glasgow rivals at the summit of the Scottish top flight to bolster their early title credentials and deepen the malaise around the Celtic team.
A superb goal from Kyziridis and a spot-kick from Shankland gave the Hearts team a 3-1 lead that the reigning champions could not recover from.
Dane Murray - one of three youngsters in the Celtic XI - scored an own goal in the early stages to put Hearts ahead at a energetic Tynecastle, and it was the 22-year-old's foul that led to the penalty.
Callum McGregor's classy first goal of the season had quickly cancelled out Hearts' opener, and Benjamin Nygren almost put Rodgers' team in front, opting for finesse over power and allowing the Hearts keeper to make a crucial stop.
But the unstoppable Hearts side regained dominance to consign the visitors to successive league defeats for the initial occasion since 2023.
It also gives the Hearts a commanding advantage at the top of the table.
The previous occasion they were this far ahead 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.
McInnes, whose Aberdeen side were runners-up to the champions on multiple times, has been at pains to play down title talk, as the club seek their maiden league title since the 1960s.
The Celtic boss has experienced this previously at the club - both perfect and shaky beginnings to a season. He's never ended as runner-up.
But on the weekend's performance, this Hearts team showed they deserve serious consideration.
Hearts started with the confidence of a side unbeaten in the league this season - fans' favourite Kyziridis delivered a ball for the striker to stab wide.
The Glasgow team didn't aid their cause with some uncharacteristic carelessness in possession and they faltered under their first real examination.
Claudio Braga's header was tipped onto the woodwork by the Celtic keeper and the follow-up from Shankland was turned into the net by the unfortunate Murray, in for the injured Cameron Carter-Vickers.
Celtic grew into the contest and started stringing passes together. From one such move, the midfielder released Tierney to set up the captain, who rolled in.
Apart from the Nygren chance, the visitors struggled to create much for striker Kenny or his replacement Shin Yamada amid the absence of stricken attackers Kelechi Iheanacho and Daizen Maeda.
The home team rediscovered their energy and adaptability in attacking from across the final third. The Greek forward, one of the finds of the club's relationship with shareholder Tony Bloom's Jamestown Analytics, struck low past the goalkeeper from the just outside the area.
Almost straight away, the defender tripped Braga in the inside right channel and the penalty taker scored. And it could've been an even more handsome win, had replacement Ageu not been denied by the shot-stopper.
Celtic's second half was partially encapsulated in two incidents involving record signing Arne 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 Belgium international was then yellow-carded for a cynical foul.
The Hearts manager: "You see how hard the players work, the team spirit. That's not sufficient on its own to win games consistently.
"What we have got, is good technical ability. You're seeing that from a lot of players who have been here before. Recent additions are eager to show that.
"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 much work ahead, plenty to improve. Following the initial fixtures is typically a benchmark of where you are."
Celtic manager Brendan Rodgers: "It's a really poor goal from our perspective. We failed to push up when the ball went back as a line so when they play it, 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 only the beginning. 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 back at home on midweek against newly-promoted Falkirk (evening kick-off). At the same time in the top division, Hearts are at St Mirren.