The off-colour Tykes, still smarting from last week's thrashing by Newcastle, conjured up a string of chances but wasted them and found Palace keeper Julian Speroni in impressive form.
Speroni produced an impressive early save to deny Filipe Teixeira only to see the Barnsley winger ruled offside.
And when Adam Hammill spun to hit a shot on the turn, it drifted over the bar before a Daniel Bogdanovic shot was blocked.
It was Palace on the break who looked certain to force their way in front when Neil Danns pulled back a dangerous ball but Nick Carle's shot was blocked by Bobby Hassell.
And Palace thought they had the ball in the net when Danny Butterfield's cross was headed goalwards by Alan Lee but Barnsley stand-in keeper David Preece managed to force the ball out.
Hugo Colace fired over for the home side from 20 yards and another Hammill shot was blocked.
Bogdanovich drilled a shot wide after Stephen Foster's head down and Speroni did well to save when Teixeira squeezed a shot through the crowded area
Palace created more danger early in the second half when Kieran Djilali fired over and at the other end Teixeira's attempt at a spectacular overhead kick from Jon Macken's header was saved easily.
A Lee volley was well held by Preece and then Barnsley striker Macken hit a tame shot at the keeper after Bogdanovich had done well.
And with time running out, Teixeira wasted another golden opportunity when Macken dragged a clever ball into his path but the man loan from West Brom smashed his shot well wide with the goal at his mercy from 12 yards out.
Speroni finished with a grandstand save after tipping Ryan Shotton's header away following Hassell's free-kick.