Derrick Favors had 22 points and 10 rebounds and Gordon Hayward added 18 for the Jazz, losers in eight of their last nine games.
Trey Burke had 11 points and 10 assists and Enes Kanter added 11 points and 15 rebounds in the setback.
Utah trailed 11-10 with 4:42 left in the first quarter, but closed the frame on a 15-7 run to take a 25-17 lead into the second. Hayward capped the burst with a 3-pointer with seven seconds left in the frame.
Nick Calathes had the Grizzlies within four, 40-36, with 3:33 left in the first half, but the Jazz managed to push their spread to double digits, 50-40, going into the break.
The Utah lead swelled as high as 13 in the third period, but Gasol's three- point play late in the quarter made it 71-62 heading into the final frame.
The Grizzlies chipped away in the fourth, eventually cutting the deficit to three, 78-75, following a Mike Miller 3-pointer with 7:18 left. The Jazz pushed their lead back to seven, 84-77, following a Favors slam, but a 12-0 burst gave the Grizzlies the lead for good.
Miller highlighted the run with a 3-pointer from the corner that tied the game.
A Favors layup stopped the bleeding and Burke was fouled with 15 seconds left, but split the free throws.
Randolph sank a pair with 11 seconds to go and Memphis held on for the win.