The Robins will take their place at Wembley on bank holiday weekend against either Watford or Hull after Lee Trundle and Michael McIndoe scored the goals to take them to the verge of a second successive promotion.
Trundle's goal was a typical finish as he bent in a shot from the edge of the area in the first period of extra time before McIndoe put the tie beyond reach with a low drive from outside the box that gave the keeper no chance.
Palace had missed a glorious chance to make their own trip to Wembley when Ben Watson hit the post from the penalty spot.
Hull will meet Watford at the KC Stadium on Wednesday and hold a 2-0 advantage from the first leg.