Hearts goalscorers Bruno Aguiar and Christos Karipidis (centre)
Hearts made toothless Kilmarnock pay for missed chances as goals from Bruno Aguiar and Christos Karipidis elevated Csaba Laszlo's side to fourth place.
The Tynecastle side had suffered a four-game Premier League goal drought but overcame this at Rugby Park.
Aguiar hit the opener from 20 yards after exchanging passes with Michael Stewart in their first decent attack.
The clinching goal arrived on 80 minutes when Karipidis headed home after Michael Stewart's free kick.
Kilmarnock had been first to threaten when Garry Hay's 30-yard free kick was easily handled by Jamie MacDonald in the Hearts goal after seven minutes.
However, Hearts were also looking dangerous and Bruno Aguiar whipped in a cross from the left that flashed across goal with David Obua lurking.
Home keeper Alan Combe was making his return from injury and he had Hay to thank for clearing after failing to collect from Andy Driver's corner.
Kilmarnock could have taken the lead when Danny Invincibile scampered into the box, but Hearts keeper MacDonald saved after Eggert Jonsson's tackle.
The visitors survived another scare on the half-hour mark when attempts from Frazer Wright, Craig Bryson and Danny Invincibile were blocked following a corner.
Jim Jefferies' side were piling on the pressure and should have gone ahead when David Fernandez was played in by Bryson, but the Spaniard shot high and well wide from the edge of the box with just the keeper to beat.
The Rugby Park men were well in command but squandered another opportunity when Hay picked out Invincibile at the back post and he should have at least hit the target instead of nodding wide.
There was a further effort on goal for Kilmarnock before half-time when Manuel Pascali couldn't get any power on his header after Invincibile's cross from the right.
Kilmarnock's David Fernandez missed a good chance to score against Hearts
Hearts, now with the wind at their backs, started strongly after the interval but still could not trouble Combe and the increasingly influential Fernandez came close from long range after cutting in following a short corner.
The visitors took the lead in the 61st minute, though, after their first incisive move of the game.
Stewart burst forward and exchanged passes with Aguiar before slipping the ball inside to the Portuguese midfielder, who fired into the corner of the net from 20 yards out.
Kilmarnock's Allan Russell sliced wide after Hay's cross had missed everyone else and the striker then headed the ball away from goal after Invincibile helped a corner into the danger area.
However, Hearts made Kilmarnock pay for their profligacy again as Stewart sent in a free kick that Christophe Berra headed across goal for Greek defender Karipidis to nod home 10 minutes from time.
They may even have added to their lead, but Combe blocked well from Christian Nade after Pascali's misplaced pass had set up the Hearts striker.
Kilmarnock manager Jim Jefferies:
"I can't believe we've lost the game, we totally dominated the first half and should have been a couple of goals ahead.
"It's a game where we've outplayed them and they've scored the goals and won the game.
"We keep missing the chances to put ourselves in front and make it easier but how can you be angry with the players?
"They've played well and worked their socks off but you've got to put the ball in the net, that's what wins games."
Hearts manager Csaba Laszlo:
"In the first half we had some luck. The opponents didn't score and had two big chances.
"The second half was better and we came out and scored. The goals were very nice.
"We played good football in the second half, which we need to to win, especially away from.
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