Key points
Rampant Hearts surged eight ahead of Celtic at the top of the Scottish Premiership to bolster their early championship claims and deepen the struggles around Brendan Rodgers' side.
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 overcome.
Dane Murray - one of three youngsters in the Celtic starting lineup - 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 spot-kick.
A stylish finish from McGregor of the season had quickly cancelled out the first goal, and Benjamin Nygren almost put Celtic in front, choosing placement over power and allowing Alexander Schwolow to save from close range.
But the unstoppable Hearts side seized control again to consign the visitors to back-to-back losses for the initial occasion since last year.
It also gives the Hearts a commanding advantage at the summit.
The previous occasion they were so far clear was in 2005-06 under George Burley, when they ended as runners-up - one of just four occasions that a team has failed to win the title after building such an advantage in the past 27 years.
The Hearts coach, whose Aberdeen side were second to Celtic on multiple times, has been working hard to downplay championship discussions, as the club seek their first top-flight crown since the 1960s.
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 Edinburgh outfit showed they need to be taken seriously.
Hearts started with the confidence of a side unbeaten in the league this season - fans' favourite Kyziridis poked a cross in for Shankland to fire off target.
Celtic didn't aid their cause with some uncharacteristic carelessness in possession and they buckled under their initial test.
Claudio Braga's header was tipped onto the woodwork by the Celtic keeper and Shankland's return ball was diverted goalwards by the hapless defender, in for the absent center-back.
The away side grew into the contest and started building moves. From one such move, the midfielder released Tierney to square for McGregor, 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 unavailability of injured forwards Kelechi Iheanacho and Daizen Maeda.
Hearts regained their intensity and versatility in creating chances in the opposition half. 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 edge of the box.
Immediately after, Murray fouled the midfielder 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 stopped by the shot-stopper.
The visitors' performance after the break was somewhat summed up in two incidents involving big-money recruit Engles.
The set-piece from Engles delivery was in sharp opposition to his midweek exploits in the Europa League win over Sturm Graz and the national team player was then booked for a professional foul.
The Hearts manager: "The effort from the squad is evident, the team spirit. That's not sufficient on its own to win games week in, week out.
"Our strength lies in, is skillful players. You're witnessing it from a lot of players who have been here previously. Some of the new signings are eager to show that.
"We're in a positive moment at the minute, but it's just one win. It's crucial for us to keep winning. We've got much work ahead, plenty to improve. After the first two rounds is typically a benchmark of where you are."
Celtic manager Brendan Rodgers: "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 should have players offside but didn't. We have got to improve with the shot.
"There's still so many points to play for. It's only the beginning. It's just nine matches. Clearly, being eight adrift 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 more quality in our play."
The Glasgow club are returning to their stadium on midweek against promoted side Falkirk (19:45 GMT). At the identical hour in the top division, Hearts are at St Mirren.
A data scientist and business strategist with over a decade of experience in transforming raw data into actionable insights for global enterprises.