Artur Boruc had to make two vital saves and both Kyle Lafferty and Kenny Miller missed decent chances.
However, it ended in a stalemate and that will undoubtedly feel a better result for Rangers than Celtic.
Rangers’ system worked well enough in the first half from a defensive point of view in the sense that while Celtic had good spells of possession they did little with it.
And in the second half they were the much better side but could not make their superiority count.
In saying that, Scott McDonald had a real opportunity – the only one of the first half it transpired – with just 15 minutes gone.
Shunsuke Nakamura worked the ball to right side for Willo Flood who produced a good near post cross which McDonald should have scored with but, fortunately for Rangers, headed wide.
The frustrating aspect for the coaches was that Rangers had good energy on either side with Davis and Fleck but Ferguson and Mendes failed to have any real impact on the match.
It was a largely thankless task for lone striker Lafferty who ran willingly but with little support.
Scrappy barely begins to describe it all and the match could only get better. Indeed there was more excitement in the first 10 minutes of the second half than there had been the whole first half.
Suddenly Rangers began to pose a threat and there was a scare for Celtic in 50 minutes.
Madjid Bougherra, of all people, popped up on the right wing and whipped over a left-footed cross which Stephen McManus nearly diverted into his own net, forcing Artur Boruc to make a great save.
From John Fleck’s corner the ball broke to Barry Ferguson but he shot wide.
Davis, easily Rangers’ best player, nearly caught Celtic on the breakaway in 56 minutes when he burst clear and played in Lafferty but his shot was too close to Boruc who saved comfortably.
Clever thinking from Davis in 58 minutes created another chance. His quick ball forward was headed down by Lafferty but Ferguson could not keep his shot down and he fired high over the bar.
Walter Smith switched things a minute later when he brought on Kenny Miller, taking off Fleck and moving Lafferty to the left.
There was clearly a sense that the game was there to be won.
Miller had the chance to play in Davis on the breakaway in 67 minutes but his ball was just too heavy and the midfielder could not reach it.
Davis was again at the heart of things in 69 minutes when he cleverly laid the ball back for Miller who was only 10 yards from goal but shot wildly wide with his left foot.
In fairness he took a whack from McManus as he shot and the Rangers men in the vicinity were convinced it should have been a penalty.
The game took its toll on Lafferty in 74 minutes when he had to go off and was replaced by Stevie Naismith.
Rangers still looked the more likely and Boruc saved Celtic again in 78 minutes.
Davie Weir made terrific contact with Mendes’s corner but Boruc brilliantly blocked his header.
Rangers had been the better team but they had their hearts in their mouths in the final minute when Celtic won a free kick in a dangerous area.
Naismith was judged to have fouled Nakamura and it was the Japanese who took it, curling his effort over the wall. McGregor spilled it but Broadfoot got back to clear.
In the end a draw was a fair result, but with their second half pressure Rangers will feel they might have won it.