Key points
The dominant Edinburgh side surged eight ahead of Celtic at the summit of the Scottish top flight to strengthen their early-season championship claims and deepen the malaise 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 title holders could not overcome.
Dane Murray - among three youth players in the Celtic starting lineup - slashed into his own net in the early stages to put Hearts ahead at a bouncing their home ground, and it was the 22-year-old's foul that led to the spot-kick.
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 Derek McInnes' irrepressible Hearts regained dominance to hand the visitors to successive league defeats for the initial occasion since last year.
It also gives the Hearts a significant lead at the top of the table.
The last time 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 failed to win the title after building such an advantage in the last three decades.
The Hearts coach, whose Aberdeen side were second to Celtic on multiple times, has been working hard to downplay championship discussions, as Hearts seek their first top-flight crown since 1960.
Rodgers has experienced this previously at the club - 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 deserve serious consideration.
The Edinburgh side started with the confidence of a side unbeaten in the league this season - fans' favourite Kyziridis poked a cross in for the striker to stab wide.
Celtic didn't aid their cause with some unusual sloppiness 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 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 a flowing attack, Sebastian Tounekti released Tierney to square for McGregor, who slotted home.
Aside from the opportunity for Nygren, the visitors found it hard to generate chances for striker Kenny or his replacement Shin Yamada amid the absence of stricken attackers their key strikers.
The home team regained their intensity and adaptability in creating chances in the opposition half. The Greek forward, one of the finds of the club's relationship with shareholder Tony Bloom's Jamestown Analytics, struck low past Schmeichel from the edge of the box.
Almost straight away, Murray tripped the midfielder in the inside right channel and the penalty taker converted. And it could've been an more comprehensive victory, had substitute Ageu not been stopped by Schmeichel.
Celtic's second half was somewhat summed up in a couple of moments involving record signing Arne Engles.
The set-piece from Engles delivery was in sharp opposition to his European display in the Europa League win over their Austrian opponents and the Belgium international was then booked for a professional foul.
The Hearts manager: "The effort from the squad is evident, the team spirit. That's not always enough to win games consistently.
"What we have got, is skillful players. You're seeing that from a lot of players who have been here previously. Some of the new signings are eager to show that.
"We've got a good thing going at the minute, but it's only three points. It's crucial for us to keep winning. We've got loads to do, plenty to improve. After the first two rounds is normally an indication of your standing."
Celtic manager Brendan Rodgers: "The second goal was disappointing from our perspective. We failed to push up when the play was recycled 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.
"There's still so many points to play for. It's only the beginning. It's only nine games in. Obviously, being eight adrift is not what we would want. The comfort is there's numerous fixtures to play.
"Our attention must turn on the present and look to find more consistency and more quality in our play."
The Glasgow club are returning to their stadium on midweek against newly-promoted Falkirk (19:45 GMT). At the identical hour in the Scottish Premiership, Hearts are at their opponents' ground.
Maya Chen is an urban planner and writer with over a decade of experience in sustainable city development and community engagement.