Key points
The dominant Edinburgh side powered eight points clear of their Glasgow rivals at the summit of the Scottish Premiership to bolster their early title credentials and deepen the struggles around Brendan Rodgers' side.
A superb goal from Kyziridis and a spot-kick from Shankland gave Derek McInnes' side a two-goal advantage that the reigning champions could not recover from.
Dane Murray - one of three youngsters in the Celtic XI - slashed into his own net early on to put Hearts ahead at a energetic their home ground, and it was the youngster's infringement that led to the penalty.
A stylish finish from McGregor of the season had swiftly equalized Hearts' opener, and Benjamin Nygren almost put Celtic in front, opting for finesse over power and allowing the Hearts keeper to make a crucial stop.
But the unstoppable Hearts side seized control again to hand the visitors to back-to-back losses for the initial occasion since 2023.
It also gives the Hearts a significant lead 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 ended as runners-up - a rare instance that a team has failed to win the title having held such a lead in the past 27 years.
The Hearts coach, whose Aberdeen side were second to Celtic on multiple times, has been working hard to downplay title talk, as the club seek their maiden league title since 1960.
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 Edinburgh outfit showed they deserve serious consideration.
The Edinburgh side started with the confidence of a side unbeaten in the league this season - the popular attacker delivered a ball for Shankland to fire off target.
The Glasgow team didn't aid their cause with some uncharacteristic carelessness in possession and they faltered under their initial test.
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 absent center-back.
The away side found their rhythm and started stringing passes together. From one such move, Sebastian Tounekti released Tierney to set up the captain, who slotted home.
Apart from the Nygren chance, the visitors found it hard to generate chances for lone frontman Jonny Kenny or his replacement Shin Yamada amid the absence of injured forwards their key strikers.
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 scouting network, fired a low shot past Schmeichel from the just outside the area.
Immediately after, Murray fouled 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 stopped by Schmeichel.
Celtic's second half was somewhat summed up in two incidents involving record signing Arne Engles.
The midfielder's wayward free-kick delivery was in sharp opposition to his European display in the continental victory 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 team spirit. That's not always enough to win games week in, week out.
"Our strength lies in, is good technical ability. You're seeing that 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 just one win. It's important for us to keep winning. We've got much work ahead, loads to do. After the first two rounds is typically a benchmark of where you are."
The Celtic boss: "The second goal was disappointing from our perspective. We didn't move when the play was recycled as a defensive unit so when they play it, they should have players offside but didn't. We have got to do better with the shot.
"Plenty of matches to play for. It's still so early. It's only nine games in. Clearly, being eight adrift is not what we would want. The comfort is there's numerous fixtures to play.
"Our attention must turn on the here and now and look to achieve greater stability and more quality in our play."
Celtic are back at home on Wednesday against newly-promoted Falkirk (19:45 GMT). At the identical hour in the top division, Hearts are at their opponents' ground.
A seasoned gaming analyst with over a decade of experience in casino slot reviews and strategy development.