With 26 seconds left in regulation, Tyler Smith hit a layup for Tennessee to tie the game at 73. Bouldin missed a shot at the other end of the floor, and Wayne Chism came up with the ball in the ensuing scramble, but couldn't get it to the Vols' end of the floor before time expired.
It was all Gonzaga (9-4) in the extra period, as Austin Daye hit a 3-pointer and four free throws to help the Zags grab their second win over the Vols for the season. Gonzaga won 83-74 on Nov. 30 in the Old Spice Classic championship in Orlando, Fla.
Daye had 20 points, and Josh Heytvelt added 15 points and grabbed 12 rebounds.
Gonzaga's win broke a 37-game home winning streak for Tennessee (9-4), the second-longest such streak among Division I programs behind Notre Dame's 43-game streak. It also helped Zags coach Mark Few avoid his first four-game losing stretch since the 2006-07 season.
Gonzaga jumped out to an early 6-0 lead, but Cameron Tatum answered with 14-straight points for the Vols.
Tennessee led by 15 points in the first half off a 3-point shot with 8:17 left by Cameron Tatum. Tatum scored a career-high 22 points, tying his previous high of 19 points by halftime.
Smith added 17 points and Chism had 15 points and grabbed a career-high 19 rebounds.
Gonzaga retook the lead with four straight 3-point baskets by Bouldin, Daye and Steven Gray, grabbing a 50-49 lead with 15:33 to go. The teams traded leads until overtime.
The Zags hit 52.5 percent from the floor and 10 3-pointers. Tennessee made only 36. 3 percent of its field goals and hit only six 3s.
It's the first time the Vols have lost a non-conference game at home under coach Bruce Pearl.