Conley, who missed seven games with the injury, keyed a 13-3 run in the final 5 minutes to carry the Grizzlies to a 15th win in 19 games.
Mike Miller came off the bench to pour in 19 points, connecting on 5-of-7 tries from beyond the arc.
Tim Hardaway Jr. scored 23 points for the Knicks, who stayed close in the second half before falling to a sixth loss in seven games.
Carmelo Anthony provided 22 points and 11 rebounds.
2014: The Year in Music [PHOTOS]