Hibee history: Talisman Kemp is the goal hero
His winner in this game was his second in four days after also getting the crucial strike against Stirling Albion the previous midweek and his only other goal came on his debut and helped defeat Dundee United.
This time he netted just before half-time from a Jim Murphy cross, getting just enough on his shot to squeeze it past the defenders on the goal line.
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Hide AdKilmarnock were in the middle of a two-legged European tie against East Germany's Lokomotiv Leipzig and put in a very poor performance watched by German coach Hans Studener.
The Ayrshiremen only created one chance in the whole 90 minutes and Brian McIlroy made a hash of it from ten yards.
In fact, Hearts should have wrapped up the points just after half-time when they were awarded a penalty for handball but Killie keeper Bobby Ferguson fisted away Murphy's spot-kick. Although he clearly moved early, no retake was ordered – but it wasn't to cost Hearts.