Two first-half goals by Shunsuke Nakamura and Georgios Samaras were enough to set the home team on the road to victory.
Further second-half goals from Scott McDonald and Aiden McGeady emphasised the home team's dominance over the newly-promoted side. Hamilton even missed a penalty late on to complete their miserable afternoon.
The only sour note for Celtic was Jan Vennegoor of Hesselink limping off after only two minutes. His substitute Samaras saw his header blocked on the line by keeper Tomas Cerny before Celtic went ahead.
McGeady's sweeping cross from the right eluded David Elebert at the back post and Nakamura controlled the ball with his thigh before volleying high into the net.
McDonald struck the post before Celtic added to their lead. The Aussie striker found Nakamura wide on the left and his square pass was side-footed home by Samaras from ten yards for his tenth goal of the season.
It looked all over for the visitors even at this stage though they briefly rallied midway through the second half when James McArthur drilled his shot wide.
Celtic squandered a number of chances before McDonald used his strength to hold off Martin Canning and the striker rolled the ball home from six yards.
Hamilton were thrown a lifeline when Gary Caldwell was adjudged to have pulled down James McCarthy as he advanced into the box.
It looked a harsh decision but it did not matter anyway as Artur Boruc pulled off a superb save from McArthur's spot-kick and then parried away his follow-up header.
There was still time for substitute Shaun Maloney to skip past Simon Mensing and Canning on the by-line before cutting the ball back for McGeady to place his shot into the corner of the goal.