Shortly after it was two courtesy of a Lee Ashcroft own goal, with the defender turning into his own net following more nice work from the returning Forrest.
Killie almost found a route back into the game when a deep cross was met by Manuel Pascali, but Fraser Foster was equal to the volley to deny the Italian.
Despite the scare, Celtic chased a third and came close through Charlie Mulgrew shorlty after the hour mark, after the midfielder was picked out by Forrest before seeing his effort coming back off the post.
Mulgrew wasn't to be denied a second time however, and after picking up Ledley's chipped pass inside the box, he swept the ball into the bottom corner to further extend the Hoops' lead.
Amido Balde rounded off the scoring with seconds remaining, with the striker cutting inside and curling his effort through the hands of Samson.