Two ahead at the interval through an own goal by Christophe Berra and a skilfully taken effort from Massimo Donati, Celtic wrapped up the points in the second half.
Scott Brown scored from close range and then Jan Vennegoor of Hesselink added a fourth from the penalty spot. Shunsuke Nakamura put the icing on the cake as the Jambos capitulated.
This was the perfect result for Celtic heading into their midweek Champions League qualifying tie with Spartak Moscow and kept the home team in touch with Rangers at the top of the SPL.
Celtic took an early lead when Scott McDonald's clever cut-back reached Nakamura and his strike deflected off Berra past the helpless Steve Banks.
The home team went further ahead after 20 minutes. Hearts carelessly gave away possession and Donati seized on the loose ball before cutting past Berra and sliding his shot low past keeper Banks.
Hearts finally showed some spark of resistance when Laryea Kingston advanced towards the Celtic penalty area before unleashing a tremendous shot which hit the post with Artur Boruc beaten. The rebound came back to Kingston, but his second effort was deflected over the bar by Gary Caldwell.
Banks then produced two outstanding saves to deny McDonald after the striker was left totally unmarked at the back post.
The stocky striker was only denied his first Celtic goal by a last-ditch tackle from Jose Goncalves and Kingston cleared a Donati header off the line as Hearts hung on for the interval.
The visitors rang the changes at the start of the second half with all three substitutes sent on.
It was one of the substitutes Andrew Driver who spurned a great opportunity to bring Hearts back into the game.
Mark Wilson was easily dispossessed and Driver raced in on the Celtic goal only to pull his shot wide of the post.
It was to be Hearts' last chance as Celtic then hit two quick goals. Aiden McGeady's cross from the edge of the area was cleverly headed down by Vennegoor of Hesselink to the advancing Brown, who slid his shot home from six yards.
A minute later Nakamura skilfully nutmegged Berra, before being pulled back by the Hearts defender. As well as conceding a penalty which Vennegoor of Hesselink lashed home, Berra was also booked to add to a miserable afternoon for the Hearts skipper.
Nakamura was not to be denied a goal when he finished off a surging run by Brown with a skilfully taken goal.
Hearts' wretched afternoon was compounded when substitute Neil McCann was stretchered off near the end.