Bradford twice held the lead but the Merseysiders in the end were good value for their point after sustained pressure in the second period.
Dean Windass, who was always a force upfront for the visitors, wasted a great chance in the 12th minute but had a hand in the opening goal in the 21st minute when he squared the ball to Richard Edghill following a throw in. The full-back found the top left-hand corner with a superb left-foot strike from fully 25 yards.
The lead lasted just three minutes though as Delroy Facey on his home debut netted at the far post from close range following a low cross by Chris Greenacre.
Bradford regained the advantage on 38 minutes. Windass headed a Mark Bridge-Wilkinson free-kick into the heart of the box and skipper David Wetherall fired home from eight yards. Alex Bruce did hook the ball clear but an assistant referee signalled it had crossed the line.
Bradford weathered a lot of pressure after the interval with Wetherall and Mark Bower doing well in central defence.
But in the 72nd minute Carl Tremarco pumped the ball back into the box and after a clearance Greenacre volleyed into the roof of the net from 10 yards for his fifth goal of the season.