Hosts Blackpool created the first chance of the encounter with eight minutes on the clock when Nathan Delfouneso shook off the attention of his marker to get in a shot at goal, which was held by Julian Speroni.
Then just a minute later, Matt Phillips beat Speroni with a curling effort, but the ball went inches wide of the upright.
It took visiting Palace a little while to impose themselves on the contest, but when they did, they almost went in front with 17 minutes played. Wilfried Zaha, who will join Manchester United in the summer, made himself some space inside the area, only to see his effort palmed around the post by Matt Gilks.
As the half drew to a close, Speroni was again called into action to deny Delfouneso for a second time after the England youth international had made a clean connection with a cross from Stephen Crainey.
In the final minute Blackpool were reduced to 10 men when the experienced Barry Ferguson was handed his marching orders for a second bookable offence.