Steve Clarke's team beat Rangers 2-1 at Rugby Park, with Eamonn Brophy converting an 89th-minute penalty after Alfredo Morelos had cancelled out an early opener from Chris Burke.
Aberdeen hit back to beat Hibernian 2-1 at Easter Road as they finished in fourth place, behind Kilmarnock on goal difference, but the Dons will also qualify for the Europa League if Celtic beat Hearts in the Scottish Cup final on Saturday.
Marc McNulty gave Hibs the lead but top scorer Sam Cosgrove equalised and James Wilson grabbed the winner before Cosgrove missed a penalty.
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