Ayala scored 21 points and added nine rebounds.
The Terps trailed the Spartans by 12 after 10 minutes.
Owusu scored 13 points in the fourth quarter to propel the Terps past the Cornhuskers.
The Terps enter the Big Ten Tournament on a two-game losing streak.
The Maryland women's basketball coach has been inspired by her father's battle with prostate cancer.
Morsell, Eric Ayala and Aaron Wiggins were named All-Big Ten honorable mentions.
The Terps made three field goals in the game's final 10 minutes.
The Terps welcomed families into Xfinity Center for the first time during Saturday's regular season finale.
Seth Lundy scored 31 points to lead the Nittany Lions to victory.