The Wolverines (22-4, 9-4 Big Ten) had dropped three of their previous four games, including a 23-point loss Tuesday night on the road against No. 8 Michigan State, and needed a half to shake off their slump.
Michigan appeared to still be struggling to get over its blowout against the rival Spartans when it trailed for much of the first half against a last-place team without a conference win.
The Nittany Lions (8-17, 0-13) led by as many as eight points in the first half. They went ahead 7-plus minutes into the game and had the lead until Trey Burke made a game-tying, off-balance fadeaway with 55 seconds left in the first half.
Penn State's Jermaine Marshall and Sasa Borovnjak each scored 17 points.
Michigan scored the first six points after halftime to take control.
Glenn Robinson III appeared to help the Wolverines pull away with eight-point leads early in the second half. The Nittany Lions, though, wouldn't wilt easily. Penn State pulled within a point midway through the half, but couldn't get the lead back.
Robinson played well following a poor performance at Michigan State, where he matched a season low with two points, while Tim Hardaway Jr. was off offensively for a second straight game.
Hardaway scored eight points on 3-of-11 shooting after equaling a career low with two points and missing 10 of 11 shots against the Spartans.
Freshman Nik Stauskas scored 18 points, giving the Wolverines the third scoring option they needed to avoid an upset.
D.J. Newbill and Ross Travis had 11 points apiece for the Nittany Lions.
Michigan welcomed back former players such as Glen Rice, who led the school to its only NCAA basketball title in 1989, over the weekend and during the game for a rededication of an aging Crisler Arena into the transformed venue that is now known as Crisler Center.
The Wolverines will have a week off before they return to the hardwood next Sunday (Feb. 24) for their matchup against Illinois inside Crisler. Tipoff is slated for 1 p.m., and the game will be televised on ESPN.
Burke, GRIII lead U-M over PSU, 79-71
The Michigan Insider Top Stories
Bush Jr. is having more 'fun' this springDevin Bush Jr. is having more "fun" in his second year at Michigan this spring.
The Michigan Insider1:05 PM
Harbaugh Recaps First Rome PracticeMichigan coach Jim Harbaugh recaps first Rome practice, thoughts on the facilities and the NFL Draft.
The Michigan Insider10:20 AM
Wangler says football is a priority in ItalyMichigan fifth-year senior Jack Wangler says football is still on the mind of his team during the Italy trip.
The Michigan Insider10:10 AM
Hudson talks improving on spring performanceMichigan VIPER Khaleke Hudson discusses his transition to a new position.
The Michigan Insider9:47 AM