After a poor first half the visitors applied intense pressure early in the second period.
Chris Burke incredibly shot over from no more than six yards and Dado Prso's header was touched on to the post by Artur Boruc.
Celtic went close with some Shaun Maloney free-kicks, with one in particular in the first half forcing Ronald Waterreus to make a superb save.
The draw leaves Rangers four points behind Hearts in the race for second place with just three games remaining.
In a low-key opening Celtic created the better chances. John Hartson fired wide before Thomas Buffel tackled Maloney well in the box.
Maloney then set off on a great run from the halfway line which ended with a free-kick on the edge of the Rangers penalty area. The striker took it himself and curled his effort around the wall only to see Waterreus make a great fingertip save.
Maloney's pass then released Maciej Zurawski but the Rangers keeper raced off his line to block the effort.
At the start of the second half Prso cut the ball back to Burke but the winger shot over from in front of goal. From Burke's cross Prso then headed goalwards only to see Boruc claw the ball on to his post.
Kris Boyd headed wide as Celtic hung on grimly.
The introduction of Shunsuke Nakamura steadied Celtic and Wattereus saved well from the Japanese player and then from Maloney.
In the final few minutes Boruc fumbled a Julien Rodriguez cross but was able to hack the ball clear to frustrate Rangers yet again.