Victory left Palace just three points adrift of safety and West Ham, one of several clubs on 13 points who could yet get drawn into a relegation battle.
Palace's new signing Marouane Chamakh put the visitors ahead with a slickly taken goal in the first half, but Stoke scored twice in four second-half minutes to claim their first points of the season.
With Robin van Persie being eased back into action after injury, Marouane Chamakh began the 2010-11 campaign as Arsenal's first-choice striker and he found the net 10 times in his first 21 games. Van Persie's return to full fitness soon cost Chamakh his place in Wenger's first XI.
Chamakh had a woeful record at Arsenal, scoring just 14 goals in 67 appearances following his free transfer from Bordeaux in 2010.
He is set to become just the third outfield player to have played in the Premier League at 40, following Teddy Sheringham and Gordon Strachan.
Arsenal manager Arsene Wenger said on Tuesday the club may seek to strengthen their striking resources in next month's transfer window ahead of the African Cup of Nations.
Ayegbeni Yakubu hit two goals on his debut as Blackburn twice came from behind to beat Arsenal 4-3 on Saturday and claim its first win of the Premier League season.
Goals from Kevin Phillips and Craig Gardener eased Birmingham's relegation fears as they moved out of the Premier League drop zone with a crucial 2-1 win over Bolton at St Andrew's on Saturday.