Two goals from Georgios Samaras allowed Celtic to close the gap on Glasgow rivals Rangers at the top of the Scottish Premier League table to one point.
The former Manchester City striker opened the scoring moments before the break by heading in a cross from Cha Du-Ri.
He then doubled the lead eight minutes after the restart when he scored from the edge of the area following a pass from strike partner Gary Hooper.
Celtic's advantage was halved four minutes from time when Killie's Danny Racchi shot into the bottom left-hand corner of the net from distance.
However, Racchi's goalscoring intervention failed to spur the visiting side to find an equaliser.
Celtic take on Rangers next week.
