The Broncs (14-7, 6-3 Metro Atlantic Athletic Conference) led by as many as 15, 35-20, with 18:21 to play before letting the Saints (7-12, 4-5) back in it.
Rider took back the lead but held it by a slim margin, 54-52, with 4:11 left. The Broncs then scored five straight capped by Mike Ringgold's jumper with 2:48 left. Siena would make it 60-57 with 1:33 to play, but Rider got a jumper and made all six of its free throws to seal it.
Gadson scored 16 points and grabbed 10 rebounds and Jonathan Thompson added 14 points for the Broncs.
Rossiter led the Saints with 20 points and 15 rebounds.