It was the fifth straight win for the Grizzlies and their 10th in 11 games.
The Timberwolves took an 83-80 lead with 5:13 to play on a layup by Kevin Love, but the Grizzlies then embarked on the surge that won them the game. Randolph scored eight points during the outburst, including the jump shot that put Memphis in front for good at 86-85 with 2:06 to go.
Love delivered his league-leading 29th double-double with 28 points and 16 rebounds. Kevin Martin and J.J. Barea contributed 14 points each.
Minnesota had won five of its previous six.