Kilmarnock sealed their first win since March thanks to two second-half goals at Tynecastle.
Hearts' Fernando Screpis missed the best opportunity of the first half when his shot was saved by Alan Combe.
Kilmarnock opened the scoring in the 74th minute when Grant Murray rose to head a David Fernandez corner into the net for his first goal for the club.
Substitute Paul Di Giacomo made sure of the win seven minutes from time when he fired home from a Paul Dalglish cross.
Hearts were looking to bounce back from Monday's 2-1 defeat at Falkirk while Kilmarnock approached the game having taken only three points from their previous five games.
Kilmarnock were first to threaten when David Lilley's left-foot shot drifted wide of Steve Banks' goal.
At the other end, Laryea Kingston tried to break the deadlock with a dipping shot that just missed the far post.
The visitors were looking to the pace of Dalglish on the wing to unlock the Hearts defence.
But, despite several crosses from the former Hibernian player, Kilmarnock failed to produce a meaningful effort on goal.
As half-time approached, Fernando Screpis missed an excellent chance to score his first goal for Hearts.
The Argentine, making his full debut for the Tynecastle side, was played in on goal by Eggert Jonsson, but his tame effort was comfortably saved by Kilmarnock keeper Combe.
David Fernandez was set up by Dalglish early in the second half, but his miss-hit shot landed at the feet of Mehdi Taouil, who fired off target.
Screpis then dispossessed Jamie Hamill and found Kingston, whose fierce effort from 25 yards drifted just over the bar.
Screpis continued to be heavily involved in the action and missed another chance when he sent his snap shot over.
Combe was then called on to prevent an own goal when Murray's misdirected header crept towards goal.
The breakthrough came 16 minutes from the end when Fernandez sent an inswinging corner onto the head of former Hearts defender Murray, who nodded home.
Fernandez was booked for his celebration following the goal, but it mattered little as Di Giacomo clinched victory late on.
The midfielder, who had replaced Allan Johnston, got on the end of Dalglish's cross and finished well past Hearts keeper Banks.
The victory was Kilmarnock's first away from home in the SPL since September.
Hearts: Banks, Thomson, Karipidis, Zaliukas, Wallace, Screpis, Stewart (Mole 64), Jonsson (Ivaskevicius 57), Cesnauskis, Kingston, Glen.
Subs Not Used: Ridgers, Palazuelos, Goncalves, Rapnik, McGowan.
Kilmarnock: Combe, Murray, Lilley, Ford, Hay, Johnston (Di Giacomo 71), Fowler, Hamill, Taouil (Locke 87), Dalglish, Fernandez (Cox 87).
Subs Not Used: Rascle, Flannigan, McInnes, Anson.
Booked: Fernandez.
Goals: Murray 74, Di Giacomo 83.
Att: 10,512
Ref: M Tumilty
BBC Sport Player Rater man of the match: Hearts' Gary Glen 6.50 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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