Morant seized control in the late stages of the fourth quarter, scoring five points in the final minute as the third-place Grizzlies closed the gap on the second-place Warriors in the Western Conference standings.
The Grizzlies are now within 2 1/2 games of the Warriors after having been eight games back on November 29.
Ziaire Williams and Tyus Jones had 17 points each for Memphis in front of a crowd of 17,800 at FedExForum arena.
Jones keyed a fourth-quarter rally that put the Grizzlies ahead for good. He connected on all five of his three-point attempts.
Stephen Curry led the Warriors with 27 points, while Klay Thompson finished with 14 points. Andrew Wiggins and Gary Payton II scored 13 each.
Morant, the 2020 rookie of the year, is just a week removed from a sprained knee that sidelined him for 12 games.