The away side saw a dogged display rewarded with an important point in their attempts to avoid the drop but never looked like stealing victory as Palace dominated a one-sided encounter.
Glenn Murray and substitute Aaron Wilbraham both missed good opportunities as Ian Holloway's men failed to score for a fourth consecutive game meaning their play-off place is not yet guaranteed.
The visitors started well and Jason Scotland tried his luck with two long-range shots inside the opening three minutes as David Flitcroft's men, wearing Palace's away kit due to a colour clash, began in confident mood.
The Reds had won three of their past four games ahead of their trip but soon found themselves on the back foot as the hosts began to dictate, Wilfried Zaha's 13th-minute header an early warning signal.
Only goalkeeper Luke Steele's acrobatics denied Andre Moritz's curling free-kick three minutes later before Murray was presented with the clearest opening of the first half.
Zaha slid in the division's leading goal scorer but Steele stood tall to keep out Murray's clipped effort after 30 minutes.
Stephen Dobbie and Wilbraham then came off the bench as the hosts began to lose momentum and the pair almost engineered a breakthrough with Wilbraham shooting just wide from the edge of the area following Dobbie's through-ball with just nine minutes remaining.
Wilbraham went even closer to clinching three points four minutes later when Jonathan Parr delivered an inviting cross but the former MK Dons striker saw his header flash past the right-hand post.
A perfect cross from Zaha gave Wilbraham a third opportunity to break the deadlock moments later but the final chance of a frustrating game for the home side was blazed over the bar.