First-half goals from Stilian Petrov and Craig Bellamy were enough to see off a spirited second-half fightback by Rangers. Steven Thompson's goal near the end gave the Ibrox side some hope but Celtic hung on, at times desperately.
This victory puts the Parkhead side five points ahead with only four games remaining and only the most optimistic of Rangers fans would anticipate their team clawing back that deficit.
Early on Ronald Waterreus had to race from his line to block Bellamy at the edge of his box. Marvin Andrews headed clear under pressure as Celtic swarmed down on the Rangers goal.
Sotirios Kyrgiakos tackled Bellamy well in the box before the Welsh striker set off on a great run. Chris Sutton's wild swipe completely missed his pass before Neil Lennon's shot was parried by the Rangers keeper.
Bobo Balde glanced a header wide before Rangers at last forced an attack but Nacho Novo shot high over.
Celtic took the lead when Petrov rose high to head home Didier Agathe's cross after John Hartson's knock down had created the chance. The Bulgarian was struck by a juice carton as he perhaps rather foolishly celebrated his goal in front of the Rangers end.
Alan Thompson's free-kick was gathered by Waterreus before Rangers finally threatened. Fernando Ricksen's curling free-kick was met by Kyrgiakos but the Greek defender was almost on his knees and could get no power in his header.
Celtic went two ahead thanks to a superb goal by Bellamy. Thompson's pass put the striker clear in a one-on-one against Kyrgiakos and he stepped inside the Greek before curling an exquisite shot into the far corner of the net.
It looked all over for Rangers at this stage but credit the Ibrox side for nearly pulling a goal back before half-time. Gregory Vignal's long-range effort was saved by David Marshall before the Celtic keeper parried a Dado Prso shot behind for a corner.
Ricksen's cross was met flush on his forehead by Andrews but crashed back off the face of the bar.
How Rangers would have liked a goal then, but at the start of the second half Thomas Buffel replaced Maurice Ross. Waterreus made a great block to deny Craig Beattie who had come on for the limping Bellamy, before Marshall did well at the other end to block Novo's shot.
Beattie should have wrapped up the points for Celtic when he broke from the half way line but curled his shot over from 20 yards.
Prso brilliantly dummied a Vignal pass, but Marshall blocked Novo's shot yet again.
Novo then rounded Marshall at the edge of the box only to see his shot cleared off the line by Jackie McNamara.
A Kyrgiakos header was then cleared off the line by Agathe as Rangers mounted ever more frenzied attacks.
The home side finally made the breakthrough when substitute Thompson fired home a close-range effort but despite frantic efforts, Celtic held on for victory.