Up 43-40 at the break, Southern Illinois (5-0) pushed its lead to 11 points just over two minutes into the second half.
Max Hooper made two 3-pointers sandwiched between two free throws for Oakland (1-2) to close the gap to five points with 1:18 left. But Beane countered with a layup and made 5 of 6 free throws the rest of the way to give the Salukis their best start since 2003.
Beane, Leo Vincent and Armon Fletcher each made three 3-pointers as Southern Illinois hit 12 of 25.
Khalil Felder, who finished second in the nation with 7.6 assists per game last season, had 27 points, 10 assists and nine rebounds for the Golden Grizzlies. He shot 10 of 17 from the field and 6 of 7 on free throws.