Jonathan Thompson scored 12 points for the Broncs (6-4), including eight as they closed the first half with a 22-8 run to lead 32-22 at the break.
Nurideen Lindsey finished with 11 points and Thompson had five assists for Rider, which led the entire second half.
Rakeem Brookins scored 12 points to lead the Saints (2-8), who have lost six in a row. Brookins missed the last three games because of protruding disks in his back. He missed all of last season with back problems.
Rob Poole and O.D. Anosike added 11 points each for Siena and Anosike had 10 rebounds.
Siena made just 6 of 17 free throws (35.3 percent) and has shot 58.3 percent (98 of 168) from the line this season.