Rookie big man Andre Drummond led the Pistons with nine points, five rebounds and two blocks off the bench, but Detroit shot just 43 percent from the floor in the first half.
Two free throws by Tayshaun Prince gave the Pistons a 2-0 lead, but the Knicks ran off 16 straight points in the next four minutes.
The Knicks turned the ball over seven times in the first quarter, but it hardly came back to bite them as they held a 29-17 lead going into the second. Anthony scored 11 points as New York shot 61 percent from the floor, went 5-of-8 from three-point range, then held Detroit to a 40 percent field goal percentage.
Shooting guard Iman Shumpert made his season debut for the Knicks and appeared in the starting lineup. He played 10 minutes and scored three points.