Minnesota shooting guard Jimmy Butler, who had a game-high 30 points, launched an off-balance 3-point attempt at the buzzer that would have tied the game, but the shot missed.
Memphis (8-15) won for the first time since Nov. 7 at Portland, prevailing for the first time under interim coach J.B. Bickerstaff. The previous head coach, David Fizdale, was fired last week.
Gasol also had seven rebounds and five assists. Guard Tyreke Evans, who hit two free throws with 12.7 seconds left to give the Grizzlies a three-point cushion, finished with 16 points, nine assists, five rebounds and three blocks.
Forward JaMychal Green gave the Grizzlies 14 points and nine rebounds, and James Ennis scored 13 points off the bench.
Minnesota (14-11) got 14 points from forward Taj Gibson and 12 each from forward Andrew Wiggins and guard Jeff Teague. Center Karl Anthony-Towns had a game-high 11 rebounds with seven points.
Minnesota shot 44.3 percent from the floor and went 4 of 17 (23.5 percent) from 3-point range. Memphis shot 47.2 percent from the field while going 6 of 21 (28.6 percent) from long distance.
The Grizzlies had a 24-8 edge on fastbreak points and owned a 41-34 rebounding edge.
Memphis was up 56-53 at halftime, but Butler led the individual scoring with 17 points.
NOTES: Minnesota coach Tom Thibodeau only used eight players Sunday in a 112-106 home victory over the Los Angeles Clippers in the first night of a back-to-back set. Every starter played at least 35 minutes. Coming into the Monday game F Andrew Wiggins was tied for third in the NBA in minutes per game at 37.0, and SG Jimmy Butler was seventh at 36.5. ... The Grizzlies' fourth-quarter rally in Cleveland fell short Saturday night as they lost 116-111, their 11th straight defeat. The effort, however, caught Thibodeau's notice. "Cleveland's the hottest team in the league, and they easily could have won that game," he said, adding, "You don't get here by accident, so if you get to the NBA, you're a great player. Every team in this league is capable of winning."