Mayo, who had 22 points in the game, hit a trey with 57 seconds to play to extend the Grizzlies' narrow lead to 94-89. Denver was limited to two free throws after that and committed one of their 23 turnovers in the closing seconds.
Mike Conley had 13 points and seven assists for Memphis and Dante Cunningham added a dozen points off the bench. The won got the Grizzlies back on track a day after their five-game winning streak was ended in Phoenix.
Denver held a 53-50 lead at halftime but was outscored 23-17 in the third quarter and shot 41 percent from the field for the entire game to 50.7 percent for the Grizzlies.