After a dismal first half Rangers applied some pressure, but Artur Boruc in the Bhoys goal made a couple of magnificent saves to deny the visitors' attack.
The Gers will probably be the happier team, taking a point away from home, but the draw means Celtic maintain their two-point lead at then top.
It was a cagey opening by both teams with no-one wanting to make a mistake.
Boruc palmed away an early John Fleck cross before Celtic should have taken the lead. Willo Flood, making his debut, turned Fleck before firing in a cross which Scott McDonald, on his own at the near post, glanced wide.
It was a bad miss by the Aussie striker in a match of few clear chances.
Soon after David Weir and Jan Vennegoor of Hesselink were booked after a clash as the Celtic striker challenged Allan McGregor.
Paul Hartley volleyed wide at the start of the second half as both teams tried to up the tempo.
Rangers went close to taking the lead on the hour mark.
Madjid Bougherra ended a driving into the Celtic area with a cross which deflected off Stephen McManus' head, but Boruc adjusted himself to make a magnificent diving save at the expense of a corner.
Steven Davis set up a chance for Kyle Lafferty but the striker's shot was straight at Boruc.
It was Rangers who were looking more likely to score and in a swift counter-attack substitute Kenny Miller's pass to Davis was just cut out by Shunsuke Nakamura at the edge of his box.
Boruc again denied the visitors when he reacted smartly to block Lee McCulloch's powerful header from a Pedro Mendes corner.
Celtic were awarded a free-kick towards the end, but although McGregor fumbled Nakamura's set-piece, the ball was hacked clear by Bougherra to leave the match goalless.