After Thomas Gravesen had put the home side ahead it was almost inevitable that former Rangers player Kenny Miller would at last open his scoring account as he added a second which killed off any Gers revival.
Play swept from end to end in the opening minutes but it was Celtic that carried the major threat. A long ball by Lee Naylor found Miller outpacing Sasa Papac but his lob over keeper Allan McGregor was just off target. Shunsuke Nakamura then warmed McGregor's hands with a powerful drive.
Rangers responded with a quickly taken free-kick from Charlie Adam which nearly caught out Artur Boruc before McGregor produced a marvellous save to keep Jan Vennegoor of Hesselink's snap-shot out.
Alan Hutton carelessly gave away possession and, although Rangers cleared the corner, it fell to Neil Lennon who had time to measure his cross.
Aiden McGeady should have scored with his header but McGregor managed to block it from point-blank range only for Gravesen to head home from almost on the line.
McGeady clipped the top of the bar with a clever shot and Celtic came close at the start of the second half with a swerving shot from Nakamura.
The visitors clearly realised they had to threaten the Celtic goal more and Dado Prso's clever pass nearly found Barry Ferguson but Boruc raced from his line to clear. Adam's clever ball to the back post then had Boruc scrambling as Rangers stepped up the pressure.
Celtic were content to hit their rivals on the break and it was McGeady's silky pass which released Miller who slid his shot home under McGregor.
Rangers continued to battle and Prso saw his header cleared off the line by Naylor before Kris Boyd's shot skimmed the bar but, by that time, it was clearly not going to be Rangers' day.
Celtic will now approach their Champions League game against FC Copenhagen on Tuesday with renewed confidence.