Julian Gamble scored a season-high 13 points and James Dews added 13 for Miami (18-9, 4-9 ACC), which had lost its past two games.
Virginia (14-12, 5-8), which lost its sixth straight game, was led by Sylven Landesberg's 27 points.
He scored eight consecutive points on three jump shots to give Virginia a 28-26 advantage during a back-and-forth first half, but Miami led 33-32 at the break.
Collins scored eight points as Miami went on an 18-5 run to turn a tie at 40 into a 58-45 lead with just over 6 minutes left.
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