Humphrey hit two from the line with 13 seconds to play and Quan Prowell missed a potential tying 3-pointer for the Tigers (14-14, 4-11). Auburn nearly got another chance when Georgia's Sundiata Gaines missed a pair of free throws with 4 seconds left when one make would have clinched victory.
But Gaines outfought two Auburn players to grab the rebound and preserve a win for the Bulldogs, who had dropped 10 of 11 games. Humphrey added two more from the line after that.
Georgia can tie South Carolina for fifth in the East with a win Saturday over Mississippi and a Gamecocks' loss at Tennessee. The Bulldogs had been 0-7 in SEC road games on the season and hadn't won at Auburn in the last six trips.
The Tigers, who missed their final six shots, are tied for last in the West with Alabama. They have dropped three in a row.
Gaines, who made just 2-of-8 shots, and Terrance Woodbury each scored 11 points for Georgia. Woodbury also had eight boards.
Tolbert's two free throws were Auburn's only points over the final three minutes after they briefly went up 52-51. The Bulldogs shot 49 percent while holding Auburn to 34.
The Tigers also made just 6-of-31 3-pointers.
Gaines had hit a 3 with 6 seconds left to give the Bulldogs a 30-27 halftime lead. They had trailed by as many as 11 points in the half, but Auburn scored just six over the final 11 minutes.