Palace settled the better of the two teams but chances were rare in a quiet start at Ewood park.
Stephen Dobbie sparked the game into life midway through the first half as he burst away from the Blackburn defence before slotting the ball into the bottom corner.
Palace continued to push for more goals after breaking the deadlock but the hosts managed to withstand the pressure.
The visitors looked lively after the break and searched for a second goal, with Mile Jedinak inches away from giving his side the lead when he headed the ball against the crossbar.
Blackburn were close to taking the lead against the run of play on the hour mark, but Morten Gamst Pedersen fired wide after collecting a loose ball on the edge of the box.
Palace looked the more likely of the two sides to snatch all three points, with Glenn Murray being denied a penalty as Blackburn held on for a draw.