St Johnstone dropped to sixth in the Scottish Premiership after a night of drama at McDiarmid Park.
The carrot being dangled in front of Perth players before kick-off was the chance to leapfrog Hearts in the standings.
But the capital visitors started far better and had the lead through Lawrence Shankland’s early penalty.
Alan Forrest doubled the advantage before Graham Carey fluffed his lines from the spot as the break approached.
There was a glimmer of hope in the second half when, thanks to another penalty, Stevie May found the back of the net.
That arrived not long before the hour mark but substitute Barrie McKay soon extended the Hearts advantage with a strike from distance.
Saints rallied and substitute Jamie Murphy made things interesting with a clever finish for 3-2 with 10 minutes left.
They could not, however, find a dramatic late leveller.
Manager Callum Davidson had made two changes from the Celtic defeat with James Brown and Daniel Phillips dropping out, replaced by Adam Montgomery and Ali Crawford.
Warnings signs were there pretty much from the off with Hearts looking far hungrier and energetic across the pitch.
Jorge Grant had clipped the outside of the post and Robbie Neilson’s side had numerous dangerous breaks forward.
One of those resulted in a 13th minute penalty being awarded - after a lengthy VAR check - when the ball struck Ryan McGowan’s hand inside the box.
Shankland, so prolific from the spot, guided low into the bottom corner despite goalkeeper Remi Matthews guessing the right way.
Not that long after Andy Halliday neatly turned inside the Perth box but blazed over the crossbar from a very promising position.
Soon Saints were forced into a change when Melker Hallberg hit the deck off the ball. He tried to give it another go but was replaced by Alex Mitchell on 24 minutes, with McGowan pushing into the midfield.
At times it was looking far too easy for Hearts to find pockets of space and they would break again with 32 minutes on the clock. Halliday guided into the path of Forrest who, with great composure, found the opposite corner.
It looked ominous but suddenly there was a route back into the game when, to the confusion of most inside the stadium, referee Willie Collum was called over to again check the trackside monitor.
Home penalty was the verdict thanks to Cammy Devlin’s handball but Carey blasted his effort over the bar and almost out of the stadium.
There was a bit of life to Saints’ performance now and Crawford’s deflected strike had Zander Clark scrambling before the former Perth shot-stopper denied May’s angled drive.
Time remained before the break for May to work into another dangerous area but he decided to cut-back instead of ping at goal himself. The danger had soon dispersed and it was very much a what could have been end to the half.
An outside chance of a revival remained and hope intensified when Saints were awarded another penalty in the 56th minute. Robert Snodgrass was punished for pulling down May.
May took responsibility this time and calmly dispatched down the middle of the goal.
Perth supporters were lifted and on the hour mark Clark received the ball inside the box, shuffled to his left but couldn’t direct his attempt on target.
Hearts made a couple of changes - one of them McKay - and he wasted little time in restoring the two-goal advantage. He drifted inside McGowan on 64 minutes and curled beyond Matthews from distance.
Immediately Connor McLennan and Murphy were introduced, replacing Clark and Crawford before, not long after, David Wotherspoon and Cammy MacPherson entered for McGowan and Carey.
Murphy hauled Saints back into the game once more with little over 10 minutes remaining. His run and neat finish across outstretched Clark made for a very interesting conclusion.
Mitchell went close with a late header but the Perth side was unable to find a way through for the equaliser.
