Price finished 6-of-9 from beyond the arc and contributed a game-high 24 points for the Huskies (10-0), who got 21 points, nine rebounds and four assists from Jerome Dyson. Gavin Edwards added 14 points and 12 boards, while Hasheem Thabeet scored nine before fouling out early in the extra session.
UConn coach Jim Calhoun. "Someone has to take charge. We won a great basketball game."
Steven Gray poured in 23 points to pace the Bulldogs (8-2), who have dropped two of their last three games. Jeremy Pargo totaled 16 points, Josh Heytvelt donated 15 points and Austin Daye scored 13.
Matt Bouldin dished to the right corner for Micah Downs, who buried the trey to give Gonzaga a 52-44 advantage early in the second half. Gray's layup stretched the lead to 57-46 with about 12 minutes left.
The Huskies, though, responded with a 12-4 burst to shrink the deficit to 61-58, and Price nailed a trey to make it 63-61 with 7:02 remaining.
Gonzaga continued to nurse a slim lead and UConn trailed 72-70 after Jeff Adrien sank a pair from the charity stripe with 1:44 left in regulation. Price made the second of two free throws with 33.1 seconds remaining, then Bouldin hit two free throws at the other end for Gonzaga with 24.7 seconds to go.
Craig Austrie's three-point try was off the mark for UConn. Dyson pulled down the offensive board and Price threw up a three-pointer over Pargo to tie the score at 74 with 7.8 seconds remaining and quiet the raucous crowd at Key Arena.
In overtime, Dyson made a pair from the foul line to give UConn an 81-77 edge and added a trey to push the advantage to seven with 1:39 left. The Bulldogs refused to go away and pulled within 87-83 on a Pargo layup with 23 seconds to play.
The Huskies held on after Price sank 1-of-2 free throws and Gray's three-point bid didn't connect.
"We lost a tough, tough game to a heck of a basketball team," said Gonzaga coach Mark Few. "We needed one rebound there and a stop. We got the stop, but just didn't get the rebound. Price hit an incredible shot."
UConn came out strong, scoring 13 of the game's first 15 points, but Gonzaga trimmed the deficit to 19-13 on a Pargo layup just under nine minutes into the contest.
After a slam by Edwards gave the Huskies a 33-23 lead with about five minutes remaining, Gray drilled a three-pointer, starting a 14-3 spurt, and Pargo's layup capped the run and gave the Bulldogs their first lead of the game at 37-36. Price sank a pair of free throws in the waning seconds and UConn carried a 38-37 edge to the break.