Key points
Rampant Hearts surged eight ahead of their Glasgow rivals at the top of the Scottish top flight to bolster their early championship claims and deepen the struggles around Brendan Rodgers' side.
Alexandros Kyziridis' fine strike and a spot-kick from Shankland gave Derek McInnes' side a two-goal advantage that the reigning champions could not recover from.
The young defender - one of three youngsters in the Celtic XI - scored an own goal in the early stages to put the home side ahead at a bouncing their home ground, and it was the 22-year-old's foul that led to the penalty.
Callum McGregor's classy first goal of the season had quickly cancelled out the first goal, and the Swedish attacker almost put Rodgers' team in front, opting for finesse over power and allowing Alexander Schwolow to make a crucial stop.
But the unstoppable Hearts side seized control again to consign the visitors to successive league defeats for the first time since last year.
It also gives the Hearts a commanding advantage at the summit.
The last time they were this far ahead was in the 2005-2006 season under their former manager, 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 working hard to play down championship discussions, as the club seek their maiden league title since 1960.
The Celtic boss has seen it all before at the club - 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 deserve serious consideration.
The Edinburgh side started with the self-assurance of a side unbeaten in the league this season - fans' favourite Kyziridis poked a cross in for Shankland to stab wide.
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 Kasper Schmeichel and Shankland's return ball was turned into the net by the unfortunate Murray, in for the absent center-back.
The away side found their rhythm and started stringing passes together. From one such move, Sebastian Tounekti released Tierney to set up the captain, who rolled in.
Apart from the opportunity for Nygren, Celtic found it hard to generate chances for lone frontman Jonny Kenny or his substitute Yamada amid the unavailability of injured forwards Kelechi Iheanacho and Daizen Maeda.
The home team rediscovered their energy and versatility in creating chances in the opposition half. The Greek forward, one of the finds of the club's scouting network, fired a low shot past Schmeichel from the edge of the box.
Immediately after, Murray fouled the midfielder in the right side of the box and Shankland scored. And it could've been an even more handsome win, had substitute Ageu not been stopped by Schmeichel.
Celtic's second half was somewhat summed up in two incidents involving big-money recruit Engles.
The midfielder's wayward free-kick delivery was in stark contrast to his European display in the Europa League win over Sturm Graz and the Belgium international was then yellow-carded for a professional 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 consistently.
"Our strength lies in, is skillful players. You're seeing that from multiple individuals who have been here before. 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 important for us to maintain this form. We've got much work ahead, loads to do. Following the initial fixtures is typically a benchmark of where you are."
Celtic manager Brendan Rodgers: "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 didn't. We have got to do better with the shot.
"Plenty of matches to play for. It's still so early. It's only nine games in. Clearly, being eight points behind is not ideal. The comfort is there's numerous fixtures to play.
"Our attention must turn on the present and look to achieve greater stability and more quality in our play."
The Glasgow club are back at home on Wednesday against promoted side Falkirk (evening kick-off). At the same time in the top division, the Edinburgh outfit are at their opponents' ground.
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