New signing Shaun Maloney was an inspiration for the home team, creating two goals for Georgios Samaras and winning the foul for Stephen McManus to score Celtic's opening goal.
The only black spot for the home team was an injury to Jan Vennegoor of Hesselink, who was stretchered off early in the match, though his absence was more than compensated by a virtuoso performance from Maloney.
This win put Celtic back to the top of the league and set-up the defending champions nicely for next week's Old Firm match.
Both teams had chances early on and Celtic keeper Artur Boruc did well to block Scott Arfield's powerful shot. Samaras failed to control a long ball which eluded Lee Bullen, before Mark Wilson shot straight at Robert Olejnik.
Celtic took the lead when Gerard Aafjes was too casual in possession, then fouled Maloney when he lost the ball. From Shunsuke Nakamura's free-kick McManus glanced the ball high past the keeper with the ball appearing to get in off his shoulder.
Michael Higden's volley was parried by Boruc before Maloney's superb pass put Samaras through and the striker rounded the keeper to put Celtic two ahead.
After the interval, John Stewart failed to get any power in his volley and Maloney should have scored from Aiden McGeady pass but pulled his shot wide.
Maloney's subtle flick put Samaras through again, but the striker shot weakly at the keeper. Samaras did better moments later, when after a slick interchange with Maloney, he slid the ball home from 20 yards, although the keeper looked slow to go down.
Olejnik did better with a marvellous double save to deny Chris Killen and then Maloney.