Deandre Mathieu led the Golden Gophers (19-12, 8-10) with 16 points and six assists, Mo Walker scored 16 points on a career-best 8-for-10 free-throw shooting performance, and Minnesota locked up seventh place in coach Richard Pitino's first season.
D.J. Newbill had 15 of his 24 points in the second half for the Nittany Lions (15-16, 6-12), who tied for 10th in the conference standings with Northwestern and drew the higher seed because they beat the Wildcats earlier this week.
Minnesota and Penn State will play on Thursday in Indianapolis, with the winner advancing to the quarterfinals to face Wisconsin.
The Gophers badly needed to win this to keep their NCAA tournament bid viable, and even another victory over the Lions four days later might not be enough to get in. Seven losses in the 10-game stretch prior to this, including defeats to the Big Ten's last two finishers, Northwestern and Purdue, a 2-7 conference road record don't look good.
But whatever happens next weekend when the brackets are filled out, the Gophers finished on a high note in honor of Hollins and the three other players who won't return next season.
Hollins had 57 points over his last three games, the most in such a stretch of his career. He scored first on a short flip shot from the lane, and the Gophers surged to a 23-3 lead that looked it belonged on the football scoreboard across the street.
Fellow senior Maverick Ahanmisi, whose playing time dwindled with the arrival of three newcomers in the backcourt that Pitino brought in, matched his career high with 13 points. He went 3 for 6 from 3-point range.
Ahanmisi played only 47 minutes total over the first 17 conference games and scored just two points.
Even Oto Osenieks, who will skip his last year of eligibility because of a persistent knee injury, joined the fun by throwing an inbound pass and promptly returning to the bench in the final minute with a wave to the crowd.
The other senior, Malik Smith, went scoreless. In his last six games, he totaled eight points on 1-for-23 shooting, including a 1-for-20 mark from 3-point range.
The Gophers led by as much as 51-26 in the second half, until Newbill helped bring the Lions back to within nine points at 55-46. But the Gophers pulled away again by hitting their free throws down the stretch. They had their fast break in full gear most of the game, thanks to 21 defensive rebounds and 10 steals that propelled it.
Tim Frazier added 14 points, going 10 for 12 from the foul line, for the Lions.
They've had some triumphs this season, with two wins over Ohio State and a victory at Indiana in one of the Big Ten's most daunting arenas for visiting teams, but they're still trying to climb out of the bottom of the conference under third-year coach Patrick Chambers. They're 12-42 in Big Ten play since he was hired.