Match summary
The dominant Edinburgh side surged eight ahead of Celtic at the summit of the Scottish Premiership to strengthen 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 title holders could not recover from.
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 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 Celtic in front, choosing placement over power and allowing Alexander Schwolow to make a crucial stop.
But the unstoppable Hearts side seized control again to hand the visitors to back-to-back losses for the initial occasion since last year.
It also gives the Edinburgh side a commanding advantage 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 ended as runners-up - a rare instance that a team has not secured the title after building such an advantage in the past 27 years.
The Hearts coach, whose Aberdeen side were runners-up to the champions on multiple times, has been at pains to downplay title talk, as Hearts seek their first top-flight crown since the 1960s.
The Celtic boss 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 deserve serious consideration.
Hearts started with the self-assurance of a side undefeated in the league this season - the popular attacker poked a cross in for the striker to stab wide.
Celtic didn't aid their cause with some unusual sloppiness in possession and they buckled under their initial test.
A headed effort from Braga was tipped onto the woodwork by Kasper Schmeichel and Shankland's return ball was diverted goalwards by the unfortunate Murray, in for the injured Cameron Carter-Vickers.
The away side found their rhythm and started building moves. From one such move, the midfielder released the full-back to set up McGregor, who slotted home.
Aside from the opportunity for Nygren, Celtic struggled to create much for lone frontman Jonny Kenny or his replacement Shin Yamada amid the unavailability of injured forwards Kelechi Iheanacho and Daizen Maeda.
The home team rediscovered their energy and adaptability in creating chances in the opposition half. Kyziridis, a standout performer 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 fouled the midfielder in the right side of the box and Shankland scored. And it could've been an more comprehensive victory, had replacement Ageu not been stopped by the shot-stopper.
The visitors' performance after the break was somewhat summed up in two incidents involving record signing Arne Engles.
The set-piece from Engles delivery was in sharp opposition to his European display in the continental victory over Sturm Graz and the national team player was then yellow-carded for a cynical foul.
Hearts head coach Derek McInnes: "The effort from the squad is evident, the togetherness. 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. Recent additions are keen to demonstrate their quality.
"We've got a good thing going at the minute, but it's only three points. It's crucial for us to maintain this form. We've got much work ahead, plenty to improve. After the first two rounds is normally an indication of where you are."
Celtic manager Brendan Rodgers: "It's a really poor goal from our perspective. We failed to push up when the play was recycled as a defensive unit so when they play it, they should have players offside but weren'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 just nine matches. Obviously, being eight adrift is not ideal. The comfort is there's so many games 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 back at home on midweek against promoted side Falkirk (19:45 GMT). At the identical hour in the top division, the Edinburgh outfit are at their opponents' ground.
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