Key points
Rampant Hearts surged eight points clear of their Glasgow rivals at the summit of the Scottish Premiership to bolster their early championship claims and worsen the malaise around Brendan Rodgers' side.
Alexandros Kyziridis' fine strike and a spot-kick from Shankland gave the Hearts team a 3-1 lead that the reigning champions could not recover from.
Dane Murray - one of three youngsters in the Celtic starting lineup - slashed into his own net in the early stages to put the home side ahead at a bouncing 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 swiftly equalized the first goal, and Benjamin Nygren almost put Rodgers' team in front, choosing placement over power and allowing the Hearts keeper to save from close range.
But Derek McInnes' irrepressible Hearts seized control again to hand the visitors to successive league defeats for the initial occasion since last year.
It also gives the Hearts a commanding advantage at the top of the table.
The previous occasion they were this far ahead was in the 2005-2006 season 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 last three decades.
The Hearts coach, whose Aberdeen side were runners-up to the champions on four occasions, has been at pains to downplay championship discussions, as Hearts seek their first top-flight crown since 1960.
Rodgers has seen it all before at Celtic - both flawless and stuttering starts to a season. He's never ended as runner-up.
But on Sunday's evidence, this Hearts team showed they deserve serious consideration.
Hearts started with the confidence of a side unbeaten in the league this season - fans' favourite Kyziridis delivered a ball 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.
A headed effort from Braga 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 found their rhythm and started stringing passes together. From one such move, Sebastian Tounekti released the full-back to set up the captain, who slotted home.
Aside from the Nygren chance, Celtic struggled to create much for lone frontman Jonny Kenny or his substitute Yamada amid the absence of injured forwards their key strikers.
Hearts regained their intensity and versatility 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.
Immediately after, Murray tripped the midfielder in the inside right channel and Shankland converted. And it could've been an more comprehensive victory, had replacement Ageu not been stopped by the shot-stopper.
Celtic's second half was partially encapsulated in two incidents involving record signing Arne Engles.
The set-piece from Engles delivery was in sharp opposition to his midweek exploits in the continental victory over Sturm Graz and the national team player 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 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. Some of the new signings are keen to demonstrate their quality.
"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 loads to do, loads to do. Following the initial fixtures is normally an indication of where you are."
The Celtic boss: "The second goal was disappointing from our perspective. We didn't move when the ball went back as a line so when they play it, they ought to be caught offside but weren'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 only nine games in. Clearly, being eight points behind is not ideal. The positive is there's so many games to play.
"Our attention must turn on the present and look to achieve greater stability and better performance in our play."
The Glasgow club are returning to their stadium on midweek against promoted side Falkirk (evening kick-off). At the identical hour in the top division, the Edinburgh outfit are at their opponents' ground.