Southern Illinois (14-2, 3-0 Missouri Valley) won for the first time in Peoria since 2012 and improved to 6-0 on the road, its best start in school history.
Beane scored seven straight points with five free throws and a jumper to give Southern Illinois a 23-13 lead and the Salukis extended it to 41-23 at the break.
Beane's dunk at the 16:19 mark gave the Salukis a 24-point lead.
Ronnie Suggs was the only player in double figures with 12 points for Bradley (2-14, 0-3). The Braves are the youngest team in Division I, with a rotation of nine freshmen and a sophomore. Ka'Darryl Bell and Scottie James were out with injuries.
The Braves' active roster has scored 1,367 career points, 269 fewer than Beane.