Mark Hudson's own goal presented Albion with an early lead but Clinton Morrison levelled on 21 minutes with his fifth goal in four matches.
Although Albion played the smarter football, Palace's spirit was 110 per cent and at the end the honours were even.
Albion could not have got off to a better start. The Eagles had already struggled to clear Jonathan Greening's corner to safety but, from the second, Palace skipper Hudson looked on in anguish as he saw his poor headed clearance glance past Julian Speroni and into the far corner.
The Baggies should have punished Palace further as a couple of sweeping passing movements saw Roman Bednar blast over with only Speroni to beat and then, shortly afterwards, Portuguese striker Felipe Teixeira did likewise with Palace's defence split wide open and Speroni only to negotiate.
Football-wise Palace could not match Albion, but the Eagles were dangerous at set-pieces and Albion were not doing themselves any favours with the regularity of free-kicks they were giving away.
It was from Ben Watson's free-kick that brought Palace on terms on 21 minutes. His inswinging ball in from the left was met by Palace's tall defender Jose Miguel Fonte who headed across the goalmouth for Morrison to net with a low shot past Dean Kiely.
For sheer effort Palace deserved that goal and indeed Watson might have put Palace in front only for Kiely to produce an excellent diving save.
After the break, Neil Warnock's Palace kept plugging away. Tom Soares cleverly cut inside and struck a fierce shot that Kiely saved well at the foot of the post.
Franck Songo'o had his shot blocked with a strong penalty shout from around the ground.
Albion needed to re-group and they had a couple of useful chances as Leon Barnett headed wide from Greening's corner and substitute Sherjill MacDonald lifted a good chance over the Palace crossbar.
But Palace had a huge let-off with 13 minutes left. A deep cross from the left seemed a routine catch for Speroni but, under no pressure, he spilled the ball under his own upright.
Palace somehow got the ball away after a real scramble and some relief for the home supporters. As a result, Palace became nervous in the last ten minutes but they did enough to frustrate Albion.
The Eagles were growing in confidence and Songo'o's cross flashed across the goalmouth with Morrison furious with himself that he was unable to meet it.