It was the visitors who made the brighter start when Chris Eagles fired an effort just wide after 18 seconds.
Eagles then came close again when he forced Julian Speroni into make a fine save after a drive from the edge of the box.
After the break it was Bolton who had the first chance when Eagles smashed a shot just wide across goal after a cross from Mears.
However, Palace were denied an opener by the post when Wilfried Zaha struck the frame of the goal after good work from Bolasie.
Zaha was again at the heart of a Palace attack when he found Murray on the penalty spot, but the latter wasted a golden opportunity.
20 minutes from time, Marcos Alonso nearly put Bolton ahead when a corner kick fell to the Spaniard, but he could only watch as his powerful drive deflected wide.
Zaha had another two chances to put his side in front, first bending an effort just wide after cutting in on the left before shooting off target from the edge of the box after some neat footwork to get away from his marker.