Celtic made it 18 consecutive victories and removed any lingering doubts that this season's championship race is over in only the first week of January.
With an 11-point lead after this victory thanks to goals from Stilian Petrov, Stanislav Varga and Alan Thompson, there is no way that Celtic would throw away such an impregnable advantage.
Rangers had Gavin Rae and Chris Burke making their Old Firm debuts, but it was keeper Stefan Klos whom the visitors had to thank with a superb instinctive save from Bobo Balde's powerful header.
John Hartson shot narrowly over before Celtic's pressure paid off. Chris Sutton dispossessed Shota Arveladze and from his pass Henrik Larsson's cross was headed home by the unmarked Petrov at the back post.
Klos made a valiant effort to keep the ball out but his fingertip save led to the ball hitting both posts before rolling over the line.
Rangers posed some threat when Burke fired in a dangerous cross which keeper Rab Douglas could only touch out but Rangers' strikers were nowhere.
The home team nearly went two up just before the interval when Didier Agathe powered his way past three defenders, but Thompson's glancing header from his cross drifted inches wide of the far post.
At the start of the second half Rangers pushed forward in search of an equaliser but Craig Moore's header from a Mikel Arteta free-kick lacked direction.
Larsson's wonderful flick with his back to goal from Thompson's free-kick came back off the post before Moore cleared for a corner. However, Celtic's second was not long delayed.
Thompson's corner was headed back across goal by Balde before Varga headed home from close range.
Michael Mols, who had come on for the injured Rae on 34 minutes, shot narrowly wide after a Balde mistake before Celtic wrapped up three points with their third goal.
The ineffective Peter Lovenkrands fouled Sutton and Thompson punished Rangers even further with his free-kick which he curled into the top corner from 25 yards.
Arveladze struck the bar near the end, but by this time Rangers were a well-beaten team.