Beane hit back-to-back jumpers with his foot on the 3-point line to give Southern Illinois a 50-45 lead with 2:31 left.
Jalen Pendleton came off the bench and scored 11 points, all in the second half, for Southern Illinois (8-11, 1-5 Missouri Valley Conference). Beane had just two points in the first half as the Salukis held a 23-20 lead.
Loyola (13-5, 3-3) was paced by Christian Thomas with 15 points. The Ramblers made just two field goals in the final six minutes of the game.
Devon Turk scored five consecutive points during Loyola's 9-2 run midway through the second half to take a 39-33 lead. Pendleton ended the run with a turnaround in the lane - the Salukis' first field goal in nearly seven minutes.