On the winning play, Brogdon took a pass from London Perrantes and launched a shot from the middle, swishing it through with 0.4 seconds left on the clock to snap a 45-45 tie.
Pittsburgh's Lamar Patterson came up short on a desperation shot at the buzzer and the Cavaliers (17-5, 8-1 ACC) wrapped up their fifth straight victory.
Brogdon ended with 16 points and Akil Mitchell provided 10 with 12 rebounds for Virginia.
The Panthers (18-4, 6-3) dropped a second straight despite 11 points and seven rebounds from Jamel Artis.
Patterson provided 10 points.