On a day where League leaders Manchester United and champions Liverpool drew at Anfield, Man City took advantage with another solid performance to gain ground in the title race.
Stones' impressive return to the fold this season was capped with a fine header off a stunning Kevin De Bruyne cross to put City 1-0 up in the first half.
With Palace lacking Wilfried Zaha due to injury, Roy Hodgson's visitors struggled for inspiration - and Gundogan added a second on the hour-mark after winning the ball outside Palace's area before expertly finishing in the top corner.
That goal knocked the wind out of Palace’s sails, and Stones scored his second of the evening as he lashed home after Vicente Guaita parried a shot from a corner before Sterling scored a fine free-kick to complete the rout.
The victory leaves City two points behind leaders Man United - and with Guardiola's side boasting a game in hand over their rivals, City have arguably marked themselves as title favourites.