Daniel Levitt scored 11 points for Cleveland State (2-2), which overcame a poor shooting performance in the first-ever meeting between the programs.
Back-to-back layups by Xavier Lundy and Jimmie Taylor trimmed Rider's deficit to 53-52 with 1:05 to play.
Edwards made 1 of 2 free throws and, after Lundy missed a jumper on the other end, Demonte Flannigan hit a pair from the stripe to make it 56-52 with 12 seconds to go.
Derek Sloan then had a steal and Edwards made the first of two free throws to cap the scoring.
Rider (0-4) made 18 of 38 (47.4 percent) field goals - while Cleveland State shot just 34 percent from the field - but made just 14 of 25 free throws. The Vikings were 23-of-32 from the free-throw line.