Palace had turned the match around after Xherdan Shaqiri had put Stoke ahead with a solo effort eight minutes into the second half.
Ruben Loftus-Cheek equalised within three minutes, his first Palace goal, turning in Andros Townsend’s pass at the far post.
Ryan Shawcross nearly restored Stoke's lead before Sakho had the final say, pouncing after Yohan Cabaye’s shot had rebounded off a post.
The win stretched Palace’s unbeaten home run to four matches and moved them to within three points of safety.
Palace: 28 Nov v Brighton (A)
Stoke: 29 Nov v Liverpool (H)