Memphis had a one-point lead midway through the third and finished the quarter with an 80-68 advantage.
Randolph scored 21 points with 14 rebounds, helping the Grizzlies to their second straight win after they had lost five straight.
Detroit, which has dropped four out of five, got 17 points from Rodney Stuckey. Memphis has won three of its last four meetings with the Pistons.
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