After Coppin's Larrisa Carter tied the game at 42 with a free throw at the 3:21 mark of the second half, Virginia responded with a 12-0 run to take control of the game.
Kelsey Wolfe, who led Virginia with 14 points, scored eight during the run, including back-to-back 3-pointers that gave the Cavaliers a 54-42 lead with 34 seconds to play.
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It was a disappointing loss for Coppin State (3-7), which led by as many as seven points in the second half.
After trailing 26-24 at halftime, Coppin State took the lead at 30-29 when Spotwood converted a pair of free throws with 14:45 to play in the game.
A layup and a 3-pointer by Ashle Craig increased the Coppin lead to 35-29 with 12:55 left in the second half.
Virginia (6-3) cut the lead to 35-33 on a layup by Simone Egwu with 10:18 to play, but Coppin State responded with a 5-0 run to take its largest lead of the game.
A free throw and a jumper by Shanice Maynard and a basket by Carter raised the Coppin lead to 40-33 with 7:46 left.
Virginia answered with a 9-0 run to take a 42-40 lead with 4:11 to play.
Maynard and Carter each hit one free throw to tie the game at 42, but Virginia then ripped off its game-deciding run.
Egwu added 11 points and 10 rebounds for Virginia, while China Crosby had seven points.
Maynard, Craig and Charlottesville native Shawntae Payne had eight points each for Coppin State.
UMES' Karona Roach and American's Alexis Dobbs finished with 15 points apiece.
The Hawks closed out the first half with an 8-0 run for a 26-24 lead at the break.
American slowly asserted itself in the second half and UMES came within 42-40 on a pair of free throws from Roach with 9:27 left and 48-47 with 5:54 left. But the Eagles went 9-for-12 from the foul line to win.
Chyress Lockhart had 11 points for the Bears (4-8), and Morgan Eye had 18 for Missouri, which closed out the final three minutes with a 7-0 run.
Wesley 81, Washington College 73: David Langan scored a game-high 21 points to lead the host Wolverines (8-4) past the Shoremen (0-9).
Wesley outscored Washington 23-11 over the closing 10 minutes of the first half for a 42-30 lead at the break. The Wolverines maintained a nine-point lead in the second half.
Stephen Poarch led Washington with 20 points, and Charlie McShane added 17.