Tommacina McBride added 10 points for the Hoyas (7-2), who trailed 37-25 early in the second half and were in danger of losing their first regular-season nonconference home game since Dec. 17, 2006.
The Hoyas responded with a 17-5 run to take their first lead of the second half, 40-39, on a runner by Rodgers with 8 minutes, 53 seconds remaining. After a Rider free throw tied the game, Georgetown pulled away with a 12-2 spurt.
Sironda Chambers scored 20 points and MyNeshia McKenzie added 16 points and 13 rebounds for the Broncs (3-3), who fell to 0-5 all-time against the Hoyas despite leading for a stretch of over 18 minutes spanning both halves.
Georgetown shot just 31.8 percent for the game.