At a glance
Rampant Hearts surged eight ahead of their Glasgow rivals at the top of the Scottish Premiership to bolster their early-season title credentials and worsen the malaise around Brendan Rodgers' side.
A superb goal from Kyziridis and a spot-kick from Shankland gave Derek McInnes' side a 3-1 lead that the title holders could not recover from.
Dane Murray - among three youth players in the Celtic starting lineup - 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 spot-kick.
A stylish finish from McGregor of the season had quickly cancelled out Hearts' opener, and Benjamin Nygren almost put Celtic in front, choosing placement over power and allowing the Hearts keeper to save from close range.
But Derek McInnes' irrepressible Hearts regained dominance to hand the visitors to successive league defeats for the first time since last year.
It also gives the Edinburgh side a significant lead at the top of the table.
The last time they were this far ahead was in 2005-06 under George Burley, when they ended as runners-up - a rare instance that a team has failed to win the title after building such an advantage in the past 27 years.
McInnes, whose Aberdeen side were second to Celtic on four occasions, has been at pains to play down title talk, as Hearts seek their maiden league title since the 1960s.
The Celtic boss 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 Hearts team showed they deserve serious consideration.
The Edinburgh side started with the confidence of a side undefeated in the league this season - the popular attacker delivered a ball for Shankland to stab wide.
The Glasgow team didn't help themselves with some uncharacteristic carelessness in possession and they buckled 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 turned into the net by the hapless defender, in for the absent center-back.
The away side found their rhythm and started building moves. From one such move, Sebastian Tounekti released the full-back to square for the captain, who rolled in.
Apart from the Nygren chance, Celtic struggled to create much for lone frontman Jonny Kenny or his substitute Yamada amid the unavailability of injured forwards their key strikers.
The home team rediscovered their energy and adaptability in attacking from across the final third. Kyziridis, a standout performer of the club's relationship with shareholder Tony Bloom's Jamestown Analytics, fired a low shot past the goalkeeper from the just outside the area.
Immediately after, the defender tripped Braga in the right side of the box and Shankland converted. And it could've been an even more handsome win, had substitute Ageu not been denied by Schmeichel.
Celtic's second half 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 continental victory over Sturm Graz and the Belgium international was then booked for a cynical foul.
Hearts head coach Derek McInnes: "You see how hard the players work, the team spirit. That's not always enough to win games consistently.
"Our strength lies in, is skillful players. You're witnessing it 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 crucial for us to keep winning. We've got much work ahead, plenty to improve. After the first two rounds is normally an indication of where you are."
The Celtic boss: "It's a really poor goal from our perspective. We didn't move when the ball went back as a defensive unit so when they pass the ball, they ought to be caught offside but didn't. We have got to improve with the shot.
"There's still so many points to play for. It's still so early. It's just nine matches. Obviously, being eight adrift is not ideal. The positive is there's so many games to play.
"We now have to focus on the here and now and look to achieve greater stability and better performance in our play."
Celtic are returning to their stadium on Wednesday against promoted side Falkirk (evening kick-off). At the same time in the Scottish Premiership, the Edinburgh outfit are at their opponents' ground.