"We had to gut it out in overtime," Hollins said.
The sixth-seeded Golden Gophers (23-14) will face No. 3 seed Stanford in Thursday night's championship game at Madison Square Garden. The Cardinal beat Massachusetts 74-64 in the first semifinal.
The top-seeded Huskies (24-11), who trailed by 15 late in the first half, sent the game to overtime when C.J. Wilcox stole the ball in the backcourt and hit the tying layup with 16.3 seconds left.
Wilcox had a good look at a potential tying 3-pointer in the final seconds of overtime, but the ball bounced off the rim. Darnell Gant put back the miss to pull Washington within a point, but after Julian Welch missed two free throws with 3.5 seconds remaining, Abdul Gaddy's desperation shot from beyond midcourt fell well short.
"Any time you're fighting back, it's always tough," Huskies coach Lorenzo Romar said. "But in the second half, I thought we were a team."
The Golden Gophers are making a long NIT run despite losing star forward Trevor Mbakwe to a season-ending knee injury in their seventh game. Senior center Ralph Sampson III has missed the last six with a sprained right knee.
Minnesota dropped six straight late in the regular season, starting with an overtime loss to Wisconsin.
"We had a tough stretch toward the end of the regular season, but everybody stayed together and everybody is on the same page," said Rodney Williams, who kept up his strong recent play with 18 points. "Once we got that loss in the Big Ten tournament, we kind of just came together and said, 'If we get into a postseason tournament, we are going to play our hearts out.' And that's what we are doing now."
Terrence Ross led the Huskies with 21 points.
Washington, which trailed by six with 91 seconds left in regulation, pulled within 59-57 on Ross' 3 with just under a minute to go, the closest the Huskies had been since midway through the first half.
Hollins let the shot clock run down before starting his drive, and Tony Wroten fouled him with 28.9 seconds remaining. The freshman guard, a 91.6 percent free throw shooter, drained both to put the Gophers up by four.
Gaddy made two free throws to pull Washington back within 61-59 with 22.8 seconds left. Instead of waiting to get fouled, Minnesota's Joe Coleman tried an extra pass, and Wilcox made him pay.
Hollins then missed a jumper and Wroten had a look at a long 3 that would have won it at the buzzer.
Minnesota turned the ball over 21 times in the game.
"Just a comedy of turnovers there," coach Tubby Smith said.
Hollins' three-point play put Minnesota up 64-61 just over a minute into overtime.
Wroten, a freshman who is Washington's second-leading scorer at 16.2 points per game, has struggled during the NIT, and he had just nine points Tuesday.
The Huskies, who finished atop the Pac-12 standings, came into the NIT looking to prove they belonged in the NCAA tournament after they became the first team to win a regular-season title in one of the six power conferences and still miss the NCAAs.
Minnesota is looking for its third NIT crown after winning in 1993 and 1998. Stanford won the 1991 title.
"I'm just so proud of their perseverance, and their ability to overcome so many distractions," Smith said of his team. "Just amazing. ... It's one of the hardest-working groups of kids I've ever worked with."