The nine long-range field goals by Douglas tied a team record for an invidual and came on 12 attempts. He scored 29 points to help the Knicks end a three-game skid.
Carmelo Anthony added 28 points and Amare Stoudemire had 16 for New York, which took an eight-point lead at halftime and owned an 18-point advantage going into the fourth quarter.
Mike Conley led Memphis with 16 points. The Grizzlies have lost three out of four.
Douglas hit 5-of-6 attempts from 3-point range in the second period. The Knicks attempted 36 shots from beyond the arc.
2014: NFL Cheerleaders [PHOTOS]
Julius Randle breaks leg during NBA debut