First-half goals by Georgios Samaras and Aiden McGeady put the home team two ahead at the interval.
Further goals by Samaras and substitute Jan Vennegoor of Hesselink in the second half added to their lead as Celtic handed out a four-goal hammering to the visitors.
It took the home team only five minutes to take the lead with Samaras cleverly chipping his shot over the keeper after Andreas Hinkel's pass reached him.
Hamilton tried to respond by Joel Thomas pulled his shot wide from 20 yards. McGeady's pass found Scott Brown, whose curling shot had Sean Murdoch scrambling across his line to save.
Celtic went further ahead when Shunsuke Nakamura's superb reverse pass put McGeady clear and the winger slipped his shot low past Murdoch.
There was a real danger at this point that Hamilton would collapse, but Murdoch made a superb save at the feet of McGeady after Samaras' pass had beaten the offside trap.
Somehow, Hamilton managed to hang on until the interval without suffering any more damage.
Early in the second half a rampaging run by Samaras ended with a cut-back to Scott McDonald, who was only denied a goal by Mark McLaughlin throwing himself in the way of the striker's shot.
Hamilton briefly threatened with Thomas' header, but Artur Boruc made a magnificent save. McGeady's shot was then held by the keeper before Celtic added a third.
Samaras picked the ball up on the left, before driving into the box and angling his shot beyond the keeper.
The visitors came close to reducing the deficit but McLaughlin's header, from James Gibson's corner came back off the bar.
Vennegoor of Hesselink broke his long goal drought when he forced the ball over the line from close range after a brilliant run and cross by Hinkel.