At a glance
The dominant Edinburgh side surged eight points clear of Celtic at the top of the Scottish top flight to bolster their early championship claims and worsen 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 overcome.
Dane Murray - one of three youngsters 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 penalty.
Callum McGregor's classy first goal of the season had swiftly equalized the first goal, and Benjamin Nygren almost put Celtic in front, opting for finesse over power and allowing the Hearts keeper to make a crucial stop.
But Derek McInnes' irrepressible Hearts 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 significant lead at the top of the table.
The last time they were so far clear was in the 2005-2006 season under their former manager, 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 last three decades.
The Hearts coach, whose Aberdeen side were runners-up to the champions on four occasions, has been at pains to play down championship discussions, as Hearts seek their first top-flight crown since 1960.
Rodgers 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 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 - the popular attacker poked a cross in for the striker to fire off target.
Celtic didn't help themselves with some unusual sloppiness in possession and they buckled under their first real examination.
Claudio Braga's header was tipped onto the woodwork by Kasper Schmeichel and Shankland's return ball was turned into the net by the hapless defender, in for the absent center-back.
The away side found their rhythm and started stringing passes together. From a flowing attack, the midfielder released the full-back to set up McGregor, who slotted home.
Aside 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 stricken attackers their key strikers.
Hearts regained their intensity and versatility in creating chances in the opposition half. The Greek forward, a standout performer of the club's scouting network, struck low past Schmeichel from the just outside the area.
Immediately after, the defender tripped Braga in the right side of the box and the penalty taker 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 record signing Arne Engles.
The set-piece from Engles delivery was in sharp opposition to his European display in the continental victory over their Austrian opponents and the national team player was then yellow-carded for a cynical foul.
The Hearts manager: "You see how hard the players work, the togetherness. That's not sufficient on its own to win games consistently.
"What we have got, is skillful players. You're witnessing it from multiple individuals who have been here before. Recent additions are eager to show that.
"We're in a positive moment at the minute, but it's only three points. It's important for us to keep winning. We've got much work ahead, loads to do. After the first two rounds is normally an indication of your standing."
The Celtic boss: "The second goal was disappointing from our perspective. We failed to push up when the play was recycled as a defensive unit so when they pass the ball, 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 what we would want. The comfort is there's numerous fixtures to play.
"We now have to focus on the here and now and look to achieve greater stability and more quality in our play."
The Glasgow club are back at home on Wednesday against newly-promoted Falkirk (19:45 GMT). At the same time in the top division, Hearts are at St Mirren.
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