Home boss Grant McCann made two changes to his starting XI, with Matty Blair and Alfie May handed starts in place of Aaron Lewis and Mallik Wilks.
The Eagles made six alterations to the team which began the 1-1 draw with West Ham, with Wayne Hennessey, Joel Ward, Scott Dann, Jordan Ayew and Max Meyer given recalls, while there was a first Palace start for loan signing Michy Batshuayi.
Eight minutes in it was the visitors who hit the front as Jeffrey Schlupp broke down the Palace left and his shot took a slight deflection off Paul Downing to leave goalkeeper Marko Marosi flatfooted as the ball flew just inside the far post.
Rovers responded to falling behind by forcing several corners, but they were unable to trouble the recalled Hennessey.
At the other end Dann headed well over from a Meyer free-kick, while Batshuayi saw a header from a corner blocked by a Rovers defender.
And in stoppage time the Eagles doubled their lead as Luka Milivojevic dinked a pass over the home defence, Andros Townsend headed the ball across the face of goal and an unmarked Meyer applied the finishing touch.
Early in the second half a swerving effort from Ben Whiteman caused Hennessey some problems and from the resulting corner Alfie May was unable to direct his header on target from six yards out.
James Coppinger was next to try his luck, from just over 20 yards out, as the home side pushed to find a way back into the game.
Herbie Kane also had a couple of efforts from distance, while Palace brought on Cheikhou Kouyate to try and shore up their midfield.
The pressure continued to be applied by Rovers, while at the other end Batshuayi took a heavy touch which allowed Marosi to make a point-blank block.
Still the hosts tried to pull a goal back, but they were unable to do so and the Premier League visitors eventually ran out comfortable winners.