Four late free throw conversions by Malik Smith in the final 30 seconds and one by Elliott Eliason with 33 seconds, enabled the Gophers (13-3, 2-1 Big Ten) to hang on after taking its first lead of the second half with 1:43 remaining.
Tim Frazier scored 20 points for Penn State (9-7, 0-3) but was unable to finish the game after injuring his right leg with 2:08 left and Penn State leading 59-57.
Mathieu forced back-to-back Penn State turnovers, including a strip of John Johnson and his ensuing basket gave the Gophers a 63-60 lead and forced Penn State to foul.
The Nittany Lions' Allen Roberts missed a game-tying 3-point shot with 1 second to go.
Minnesota, which has won 30 out of 40 games in its series with Penn State, also got 11 points and 12 rebounds from Eliason.
Gopher MBB Media Day Recap
Catch some of the sights and sounds from Tuesday's media availability at Williams Arena.
Gophers to Host Media Day Tuesday
The Minnesota men's basketball team will hold its annual media day this Tuesday at Williams Arena.
Homecoming Tip-Off Draws Crowd
Minnesota's men's and women's basketball teams gave fans a season preview with an open scrimmage and autograph session.