Eurosport - Liam Kelly converted from the spot to sink Hearts
There was little between the teams in the first half, which saw Kelly score from the spot in the 26th minute after Gorgie defender Andy Webster had fouled James Dayton.
However, the Tynecastle men laid siege to the Killie box at times in the second period only to be denied by dogged defending and some fine saves from keeper Cammy Bell.
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