Midfielder David Fox brought Pool back to life in the 68th minute when he latched on to a rebound, after Stephen Crainey's free-kick had crashed into the Palace wall.
Fox collected the ball at an acute angle, turned his man, and fired into the bottom corner.
From then on, it was virtually all Blackpool as Keigan Parker clipped the outside of a post with a 30-yarder and that was swiftly followed by some desperate Palace defending, which saw efforts from Parker and Scott Vernon cleared off the line.
Palace keeper Julian Speroni also came in to the rescue act when he incredibly clawed away a Shaun Barker point-blank header.
Blackpool were down to just 16 fit players before the kick-off and it certainly showed in the first half.
Palace's expensive squad passed the ball round with ease and created a host of good chances which Jamie Scowcroft and Dougie Freedman failed to convert.
It seemed only a matter of time before Warnock's side went ahead and that came in the 58th minute when Danny Butterfield charged down the flank where he had been given plenty of room, courtesy of an injury to his marker, Gary Taylor-Fletcher, a few minutes earlier which had left Taylor-Fletcher limping.
Soares was to turn from hero to villain a few minutes later when he lashed out at Blackpool sub Andy Welsh and stupidly got himself red-carded, putting even more pressure on the visitors' defence as Pool hunted for a winner.