A fantastic shot from Scott McDonald in the 58th minute was all that separated the teams at Ibrox.
The match failed to live up to its billing and the conditions played their part in that, with the pitch seemingly frozen in places.
It was a scrappy encounter throughout, but Celtic won by taking one of the few goalscoring opportunities for either side.
The home side started in furious fashion and Steven Davis fired narrowly wide in the first minute.
Rangers had the ball in the net in the tenth minute when the Celtic defence failed to clear a Davis corner from the left and Kirk Broadfoot, Artur Boruc and the ball ended up in the net together.
However, referee Craig Thompson blew for a foul by Broadfoot on the visiting keeper.
Kenny Miller and Georgios Samaras exchanged chances before Boruc saved a deflected shot by Barry Ferguson, but it was a poor first-half showing and a fair scoreline of 0-0 at half time.
The home side started the second half as they did the first and Rangers should have found themselves infront in the 46th minute when a brilliant Ferguson pass sent Kris Boyd clear on goal on the right.
However, Boruc pulled of a great save to deny Boyd and the rebound bounced off the striker and out for a goal-kick.
On 55 minutes, Gary Caldwell brought down Kenny Miller on the edge of the box but the resultant free-kick from Boyd was blocked by the Celtic wall.
Three minutes later, Celtic netted superbly against the run of play.
A long ball was nodded on by Samaras and McDonald turned Broadfoot brilliantly before firing a right-foot shot past Allan McGregor and high into the Rangers net.
Paul Hartley had a long-range effort easily held by McGregor on 75minuites and Samaras could have added to Celtic's lead with five minutes remaining but found the Scotland keeper again in the way.
A team effort from substitute Nacho Novo was all that Rangers created despite plenty of late possession and Walter Smith will be bitterly disappointed to find his side a long way back in the race for the title when they could have been neck-and-neck with Celtic had the result been reversed.