Maia scored nine of his points in the first half as Brown (6-2) took an 11-point lead into halftime. American (3-5) went on a 12-4 run to pull within one, 58-57 with 8:07 remaining. Brown answered with McGonagill's 3-pointer, which capped a 7-1 run, stretching the Bears' lead to 65-58.
A pair of free throws by Charlie Jones pulled American within two points, 69-67 with 2:01 to play, but the Eagles finished 0 of 4 from the floor.
John Schoof had a game-high 15 points for American, leading four in double figures.
Authorities say former Michigan State basketball player Keith Appling has been charged with carrying a concealed weapon and other crimes.
Point guard Jaylen Fisher, who reopened his recruitment after coaching changes at UNLV, has committed to TCU over a long list of schools.
Forward Kennedy Meeks, who has averaged 9.4 points and 6.5 rebounds at North Carolina, has pulled out of the NBA draft and will return to the Tar Heels.