First, Garry Hay's curling effort from left midfield was headed to safety before Merouane Zemmama's 25-yard effort went well over Mark Brown's crossbar.
Kilmarnock made two changes from the side that defeated Dunfermline 3-2 last weekend with GarryHay and Slovenian Leon Panikvar preferred to Rory McKeown and Alex Pursehouse.
Defender GarryHay was also able to turn out for the Ayrshire side he won his appeal against suspension following a red card in Killie's win at Motherwell.
Gibson himself then went for goal after a GarryHay free-kick, but his first effort from the edge of the area was deflected back to him and he put his second over the bar.