Palace enjoyed the majority of possession early in the game but Blackburn looked solid in defence.
However, Rovers were close to taking the lead when Jordan Rhodes found space on the edge of the box but his effort on the turn flew over the crossbar.
Stephen Dobbie broke the deadlock in the 26th minute as he broke free of a couple of Blackburn defenders before slotting the ball into the bottom corner from 18 yards out.
Blackburn failed to respond following the goal and they could have been further behind but Dobbie was unable to get enough power on a free kick to double his tally for the afternoon.
The hosts managed to level the scores just before the break when Rhodes was left unmarked to fire in an equaliser.