All the goals arrived in the second-half with Richard Cresswell firing Stoke in front on 49 minutes before Dougie Freedman levelled for Palace two minutes later.
It went all downhill from there for former Sheffield United boss Warnock and his Palace team as Cresswell scored again and substitute Jon Parkin capped an excellent Stoke show with a third.
After a goalless first-half where both Paul Dickov and Clinton Morrison missed good chances, Stoke opened the scoring four minutes after the break.
A quickly taken free kick by the left corner flag saw skipper Dominic Matteo cross to the far post for Cresswell to simply stretch his neck muscles and head easily past Julian Speroni.
Within two minutes Freedman levelled for Palace with a neatly taken goal following a pass from Jose Miguel Fonte. It was the hit-man's first league goal of the season
Stoke restored their lead on 59 minutes as Cresswell volleyed into the net after Liam Lawrence cut inside and struck the foot of the post.
Stoke completed a fine win when Ryan Shawcross slammed a tremendous shot against the crossbar but Parkin was first to react with the rebound as he rose to head the bouncing ball over the line.
The Eagles now linger just two places and two points above the relegation zone, giving Warnock a task almost as herculean as that which Iain Dowie's 2004 team faced and won.
Up into fifth go the Potters, where they would want to be at the end of the season having come so close to making the play-offs last term.