There were two changes in the Bluebirds line-up with Kevin McNaughton and Trevor Sinclair replacing Alan Ramsey and Peter Whittingham.
City should have taken the lead in the sixth minute when Paul Parry threaded a ball through to Steve Thompson but, with only Dean Kiely to beat, he blasted high over the bar.
The Bluebirds took the game to Albion and were well on top when the midway point in the opening period was reached.
However, in the 24th minute City failed to clear their lines and the ball bobbed about in the danger area before reaching Zoltan Gera, but Glenn Loovens cleared off the line.
Two minutes later, Ishmael Miller had Peter Enckelman scrambling to push behind at his near post as the Baggies suddenly raised their game.
Warren Feeney started the second half in place of the out-of-touch Thompson and Whittingham followed three minutes later for Parry, who appeared to have a slight injury.
Miller turned Roger Johnson in the 54th minute and struck his shot against the angle with Enckelman beaten, while Feeney's short stay on the pitch ended at the same time as he limped off to be replaced by Riccardo Scimeca.
The Baggies made a double switch in the 67th minute with Roman Bednar and Chris Brunt coming on to pep up their attack.
They were soon joined by Kevin Phillips as the visitors went for the win they needed to keep their automatic promotion hopes high.
Bednar should have done better with a close-range header in the 85th minute, but the final whistle came with both sides fully deserving a point apiece.