At a glance
The dominant Edinburgh side surged eight points clear of their Glasgow rivals at the top 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 Derek McInnes' side a two-goal advantage that the title holders could not overcome.
The young defender - one of three youngsters in the Celtic starting lineup - slashed into his own net in the early stages to put Hearts ahead at a energetic their home ground, and it was the youngster's infringement that led to the spot-kick.
Callum McGregor's classy first goal 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 consign Celtic to back-to-back losses for the first time since 2023.
It also gives the Edinburgh side a commanding advantage at the summit.
The previous occasion they were this far ahead was in 2005-06 under George Burley, when they ended as runners-up - one of just four occasions that a team has not secured the title having held such a lead in the past 27 years.
The Hearts coach, whose former team were second to Celtic on four occasions, has been working hard to downplay title talk, as the club seek their maiden league title since 1960.
The Celtic boss has seen it all before at Celtic - both flawless and stuttering starts to a season. He's yet to finish second best.
But on the weekend's performance, this Edinburgh outfit showed they need to be taken seriously.
Hearts started with the self-assurance of a side undefeated in the league this season - the popular attacker delivered a ball for the striker to stab wide.
Celtic didn't help themselves with some unusual sloppiness in possession and they faltered under their initial test.
Claudio Braga's header was touched on to a post by Kasper Schmeichel and the follow-up from Shankland was diverted goalwards by the unfortunate Murray, in for the injured Cameron Carter-Vickers.
The away side grew into the contest and started stringing passes together. From one such move, Sebastian Tounekti released the full-back to square for the captain, who slotted home.
Apart from the Nygren chance, the visitors struggled to create much for lone frontman Jonny Kenny or his replacement Shin Yamada amid the unavailability of stricken attackers Kelechi Iheanacho and Daizen Maeda.
The home team rediscovered their energy and versatility in attacking from across the final third. Kyziridis, 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.
Immediately after, the defender fouled Braga 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 the shot-stopper.
The visitors' performance after the break was partially encapsulated in a couple of moments involving record signing Arne 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 booked for a cynical foul.
The Hearts manager: "You see how hard the players work, the togetherness. That's not sufficient on its own to win games week in, week out.
"Our strength lies in, is good technical ability. 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 only three points. 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 your standing."
Celtic manager Brendan Rodgers: "It's a really poor goal from our perspective. We didn't move when the ball went back as a line so when they pass the ball, they should have players 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 just nine matches. Obviously, being eight adrift is not what we would want. The positive is there's numerous fixtures to play.
"We now have to focus on the present and look to achieve greater stability and more quality in our play."
The Glasgow club are returning to their stadium on midweek against newly-promoted Falkirk (evening kick-off). At the same time in the Scottish Premiership, Hearts are at their opponents' ground.
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