Jaleel Cousins had 11 points, and Jahmal McMurray and Nehemias Morillo added 10 points each for South Florida (7-22, 4-12), which had a two-game conference winning streak end. USF hasn't won three conference games in a row since 2012.
UConn extended a 15-point halftime advantage to 43-16 four minutes into the second half.
Sterling Gibbs hit a 3, and Brimah had a slam and rebound basket as the Huskies put together a 15-3 run.
Miller scored 12 of his points in the second half.
Brimah and Gibbs had six points apiece as UConn led 28-13 at halftime.
Gibbs finished with nine points.
Brimah had consecutive dunks to put UConn up 21-11 with 4 1/2 minutes left in the first half. Fast-break baskets by Purvis and Daniel Hamilton, and Gibbs' 3-pointer made it 28-11 two minutes before the break.
South Florida shot just 15.4 percent (4 for 26) during the opening 20 minutes. The Bulls' first three field goals came from 3-point range. McMurray hit USF's first two-point basket 31 seconds before halftime.
UConn: The Huskies lead the all-time series 16-2. ... UConn outscored USF 18-2 in the paint during the first half.
South Florida: USF had stretches of 12 and nine missed shots in a row during the first half. ... McMurray has scored in double digits in each of his last 21 games.
UConn: The Huskies host Houston Sunday.
South Florida: The Bulls play their home conference finale Wednesday night against East Carolina.