The champions raced into a 3-0 lead before the half-hour mark and a late Gary Hooper strike completed Neil Lennon's 100th win in charge of Celtic.
Hearts had a chance to cut the deficit in the dying minutes but Celtic keeper Fraser Forster, immense between the sticks all night, pulled off another stunning save to beat out Marius Zaliukas' spot-kick.
"Celtic were clinical tonight, very clinical," he said.
"We put a lot into the game but you cannot hide from the scoreline although it is not a true reflection on the game.
"The stats were very even but Celtic have very good players and when they're on song like tonight they are very difficult to play against.
"I thought the attitude of our players was great. They never gave up and there were many positives to take from the game.
"I thought Ryan McGowan was excellent. He had a great game going forward all night. Jason Holt was another to have a great night.
"It also has to be said that Fraser Forster was different class. He made a brilliant save from the penalty and another from a free-kick as well as one or two others. He is a great form at the moment."