Ryan Evans had 17 points and 11 rebounds for Wisconsin, which went 15 for 17 from the free throw line in overtime.
Rodney Williams and Andre Hollins guided a frantic comeback by the Gophers in the final minutes of regulation after they fell behind 49-36. The Badgers made only one basket over the last 9 minutes of the second half, a putback by Jared Berggren with 7:44 remaining.
Both Austin Hollins and Andre Hollins had shots to win the game in the final seconds for Minnesota, but the Badgers dodged that scare, refocused in overtime and improved to 19-0 this season when leading or tied with 5 minutes left.
They went just 2 for 12 from 3-point range after halftime.
Andre Hollins had 20 points, including five 3-pointers, and six rebounds for Minnesota, while Williams had 16 points.
Coming off a defeat by Ohio State that stopped their six-game winning streak, the Badgers have two more losses than the Buckeyes and thus needed a victory over their border-state rival to keep up in the Big Ten race. The road might have been the best place for them to try to rebound. Wisconsin has the conference's best regular-season road record since coach Bo Ryan was hired in 2001. The Badgers are 8-2 away from the Kohl Center this season.
The Gophers have been trying to climb above the middle of the pack since recovering from their 0-4 start, one of five teams that began the night with five or six losses in the conference. This started a stretch of five home games out of the last seven on the conference schedule, but including their rematch with the Badgers in Madison in less than three weeks, the Gophers were staring at five foes ranked in the Top 25.
Taylor had only one other 20-point game this season, when he scored 28 against Michigan State, and the preseason All-America hasn't been as productive or dominant as he was as a junior. Even his free throw shooting is down by 10 percent.
This was one of those signature games, though, for the spunky senior. After going 4 for 4 from 3-point range in the first half, he hit another one early in the second to push Wisconsin's lead to 37-26. About 5 minutes later he started a fast break, determined to finish it, he weaved back and forth around the Gophers before flipping the ball in for a nifty layup and a three-point play to make it 45-33.
After drawing the foul and landing on the court, he sat up and struck one of those it's-my-night poses by folding his arms across his chest and staring confidently at his teammates.
The Gophers couldn't crack that dogged Wisconsin defense, averaging a nation-best 49.8 points entering the game. After a spirited first half, they started fumbling passes, committing egregious turnovers and firing ill-advised 3-pointers. The Badgers are third in the nation in 3-point defense, and while the Gophers have improved from behind the arc that's not their strong suit.
They didn't wilt, though, and Williams and Andre Hollins sandwiched baskets around an offensive foul on Taylor. Andre Hollins beat the shot clock with a 3-pointer to bring the Gophers within two, and Austin Hollins tied the game with 1:02 left on two free throws to send a deafening roar through the arena.
Berggren's 3-pointer from the corner clanked off the side of the rim, setting up the final possession.
Wisconsin brought records of 208-18 under Ryan and 15-1 this season when leading at halftime, and they took a 32-24 edge to the locker room. The Gophers were averaging nearly 16 assists per Big Ten game, the best in the conference, but had only two before the break. Freshman Joe Coleman, endangering his starting spot, was scoreless for a third straight game.