They got there in the end but this was an anxious finale for a Hearts side who took all three points against a Kilmarnock side who will be frustrated to have taken nothing from their trip to Gorgie.
It is a win, though, that has contrasting fortunes for both managers; it eases the pressure on Neil Critchley whose side leapfrog Kilmarnock and moved within three points of a top six place. For Kilmarnock, it is a defeat that leaves them second-bottom of the table, a point behind Ross County.
Killie looked hungry and energetic in the opening exchanges but quickly had their winds clipped with Kabungu netting with little over seven minutes on the clock.
It was an odd goal for Killie to lose – and indicative of what was to follow for much of the afternoon.
Grant’s sliced volley fell for James Wilson with his scoffed effort making its way to the backrest for Kabungu to prod into the back of the net for his third goal in just two games.
Hearts were dealt a blow when Craig Hackett had to limp off in some discomfort just minutes after the opener.
It might have got worse for Killie from there on in with Hearts dominating much of the opening period. Wilson ought to have doubled their lead when he had an effort blocked while McCart had a header from Blair Spittal’s free-kick chopped off when VAR ruled he was offside.
Other than a Wales header that came off the legs of Craig Gordon, Kilmarnock failed to offered too much of an attacking threat.
With derma McInnes increasingly exacerbated on the touchline, they emerged from the break wit the bit between their teeth, quickly restoring parity.
Marley Watkins was the architect, crossing into the box for Wales to volley low into the bottom corner.
Two goals in just four minutes turned the tide back in Hearts’ favour, however. McCart restored their lead when he powered a James Penrice corner into the net with Grant then turning in their third, in a nightmare moment for Killie number two Kieran O’Hara.
Grant slide into get himself on the end of a low cross with the ball blocked and rising. O’Hara came to collect but Grant, on his feet, managed to manoeuvre himself in front of the stopper and head into the net.
Killie, to their credit, kept at it with Murray pulling them right back into it.
Danny Armstrong, who started on the bench after speculation this week linking him with a move to Tynecastle, whipped a ball into the box for Murray to get above Adam Forrester and net.
As frustration grew, Musa Drammeh looked to give Hearts a little more breathing space when he clipped the outside of the post after a beautiful ball through from Kabungu had sent him in behind the Killie defence.
Armstrong was always a threat with the winger winning a free-kick after slipping the ball through the legs of Yan Dhanda. He tried his luck with an effort on goal, forcing Gordon to gather at his front post as Kilmarnock pushed for a leveller.
They got closer, still, with David Watson forcing a fine save from Gordon from the edge of the box after the veteran keeper got down smartly to push a ball that looked destine for the bottom right-hand corner around the post.
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