Mike Miller added 14 points for the Grizzlies, while Darko Milicic finished with 10.
Al Jefferson and Marko Jaric both scored 17 points to lead Minnesota with Jefferson also grabbing 15 rebounds. Rashad McCants added 15 points and Ricky Davis had 14, all in the first half, for the Timberwolves.
Memphis went on a 15-0 run in the fourth quarter to take a 98-86 lead. Gay had six points in the stretch, including an alley-oop dunk off a fastbreak that started with a Minnesota turnover.
The Timberwolves went more than six minutes without scoring until McCants' layup with 1:19 left.
Navarro keyed the fourth-quarter comeback with consecutive 3-pointers that tied the game at 81.
But Memphis would not overtake the Timberwolves until Kyle Lowry scored from the lane with six minutes left for an 87-86 lead.
The Timberwolves led by as many as 16 points in the first half as Jefferson scored 13 points, hitting all four shots from the field, and grabbing 12 rebounds in 13 minutes.
Minnesota shot 56 percent from the field in taking a 61-47 halftime lead.
Despite promises of a faster pace from the Grizzlies under new coach Marc Iavaroni, the Timberwolves outscored Memphis 10-0 on fastbreak points in the first quarter.
Memphis did show its running ability early in the second half, cutting the lead to 67-63. But the Grizzlies also missed opportunities during the stretch as Pau Gasol muffed a dunk, Gay missed a layup and a tip, and Miller misfired on an open 3-pointer on the break.