Rovers almost took the lead against the run of play in the first half when Dickson Etuhu headed goalwards only to see his effort come off the crossbar.
The hosts did make the breakthrough before the interval as Glenn Murray met Owen Garvan's cross to head in off the bar.
Murray almost doubled his personal tally 10 minutes into the second half after Zaha had forced a save from Paul Robinson, but he couldn't capitalise on the rebound.
Murray's second goal of the day did come eventually, however, as he converted from the spot having been brought down inside the box.
He should have completed his hat-trick moments later when Palace were awarded another penalty, but his effort was straight down the middle.
Blackburn came within inches of getting a goal back in the closing stages when Ruben Rochina latched on to a short corner, but his effort smashed against the bar.