Anthony provided 27 points on 10-of-17 shooting and pulled down seven rebounds while Stoudemire came off the bench to pump in 20 points for New York, which led wire-to-wire.
Tyson Chandler collected 20 rebounds and scored eight points as the Knicks racked up their eighth triumph in 10 contests overall.
Jose Calderon, acquired last week in a trade from Toronto, made his debut for the Pistons, putting in a team-high 15 points on 7-for-12 shooting in the loss.
Greg Monroe supplied a double-double of 13 points and 10 rebounds for Detroit.
Celebrity Couples of 2014 [PHOTOS]