The Seasiders went ahead early on and had the better of the play until Tommy Black's equaliser, but were unable to overcome an injury to defender Chris Clarke.
The home side's goal came after just nine minutes courtesy of an own goal by Tony Popovic who directed the ball into his own net as he tried to clear a Richie Wellens corner.
The lively Black caused most of the problems for Palace and could have equalised shortly after the goal after being gifted the ball by Clarke, called up at the last minute to replace injured veteran Colin Hendry. However, Black shot just wide.
The game was becoming increasingly niggly, not helped by an inconsistent refereeing performance from Mr Webster, best summed up by an unlikely yellow card given to John Murphy after the Blackpool striker appeared to have won the ball with a fair tackle.
The Seasiders almost doubled their advantage shortly before half time when Leam Richardson teed up Danny Coid in the area but the young full back shot narrowly over the bar.
A half-time reshuffle by Palace boss Trevor Francis saw Ade Akinbiyi replace Danny Granville and the attacking substitution paid dividends 11 minutes into the half.
With Clark off injured Blackpool dropped Keith Southern into the back four and he was beaten by Danny Butterfield who crossed to find Black unmarked in the area and his volley hit the back of the net.
Worse was to come for Steve McMahon's side six minutes later when Black was pulled down in the area and stepped up to take the penalty himself.
The striker's effort was saved brilliantly by Phil Barnes but the goalkeeper was let down badly by his team-mates who allowed Black to fire home the rebound.
Trevor Francis said: "We were facing a Cup exit at half time but the change helped us and we took the game to them."