The Cavaliers remained the chief challenger to No. 1 Syracuse in the Atlantic Coast Conference by winning their sixth straight game.
Brogdon produced his first double-double at Virginia with 17 points and a career-best 10 rebounds. He also had seven assists.
Anthony Gill and Justin Anderson had 13 points each for the Cavaliers, although Anderson became the first Virginia player to foul out of a game this season.
Virginia built a 19-point halftime lead and repelled a Boston College comeback bid while improving to 18-5. The Cavaliers are 9-1 in the ACC and trail unbeaten Syracuse by half a game.
Boston College (6-16, 2-7 ACC) scored 12 straight points inside the 5-minute mark to briefly cut its deficit to six points. Ryan Anderson led the Eagles with 20 points.