Sundiata Gaines had 24 points for Georgia (12-13, 3-9), which led 38-37 at halftime.
The Commodores made 17 of their first 24 shots in the second half to take an 86-68 lead on a 3-pointer by Foster with 4:38 remaining.
Vanderbilt completed a season sweep of Georgia for the first time since the 1999-2000 season.
"We got on a little bit of a roll in the second half," Commodores head coach Kevin Stallings said. "I think we wore them down a little. We had a better look to us offensively and defensively."
Gordon hit four 3-pointers in the first half as the Commodores took an eight-point lead. But for the half, Vanderbilt shot only 40 percent.
Gaines scored eight points in a span of 2:30 late in the first half to pull the Bulldogs within 34-33. A 3-pointer by Terrance Woodbury with 30 seconds left in the half gave the Bulldogs the 38-37 lead.
"We were winning, so we were in good shape, but we knew it would be a 40-minute game," Felton said. "I think all our players realized the second half would be much tougher than the first half."
Gordon's play was key for Vanderbilt. The senior guard hit a career-high seven 3-pointers and had the most points he's scored in a game since getting 30 against Tennessee as a freshman.
Gordon's 3-pointer with 14:33 left was his sixth in seven attempts and handed the Commodores a 59-47 lead, their largest of the game to that point.
"Most of the time, my teammates found me and I was just able to knock them down," Gordon said.
Georgia made a final charge, cutting the lead to 71-62 with 8:42 left on a jumper by Zac Swansey. Vanderbilt answered with a 7-0 run, highlighted by five points from Foster, to finish the Bulldogs.
Georgia has lost eight of nine games.
"It's never easy against Georgia," Stallings said. "They played hard, played physically and made some shots. We're happy with the win. We did not expect this to be easy."