Taurasi, the only returning starter from last season's national championship team, made a 3-pointer with 7.5 seconds left to send it to the extra period tied at 56-56. The All-American also made a jaw-dropping 3-pointer from about 60 feet away as time expired in the first half to put UConn ahead 29-26.
The Huskies (12-0) have the second-longest winning streak in NCAA history, behind Louisiana Tech's 54 straight victories from 1980-82.
UConn leads the series against Tennessee 10-6, and Saturday marked only the third time in the rivalry's history that one of the schools wasn't ranked No. 1.
In the tightly contested game, Tennessee (9-3) made the first move to pull away midway through the second half. Tied at 41-41, Kara Lawson scored nine points in a 13-5 Tennessee run to put the Lady Vols ahead 54-46 with 5:17 left. The eight-point edge was the biggest for either team.
Led by Taurasi, the Huskies responded with an 8-0 run over the next five minutes. She scored three points in the spurt and made a tap-pass beneath the basket to Jessica Moore, who converted the layup. Ann Strother's driving layup capped the spurt and pulled the Huskies within a point with 43.8 seconds left to play.
Shyra Ely brought Tennessee back, splitting the defense in the lane for a layup with 17 seconds left. On the UConn inbounds, Taurasi took a feed from Maria Conlon and calmly sank her 3-pointer with 7.5 seconds left.
In overtime, Shanna Zolman made a pair of free throws to give Tennessee at 58-56 lead. Conlon countered for UConn with a 3-pointer. Taurasi then rebounded a miss by Tennessee. With Lawson guarding her, Taurasi backed into the lane and hit a turnaround jumper for 61-58 UConn lead with 2:35 to play.
Zolman hit another jumper with 1:22 left to put Tennessee back in front by a point. Taurasi responded with the game-winner. Tennessee had one final shot with 1.9 seconds left, but Lawson's jumper bounced off the rim.
The Lady Vols outrebounded the Huskies 42-39, but leading rebounders Gwen Jackson and Ashley Robinson combined for only four. Robinson finished with 15 points and Lawson chipped in 13.
Tennessee will travel to Norfolk, Virginia on Tuesday night to meet Old Dominion at 7pm EST.