Marshall made four 3-pointers but it was a 2-pointer with 6:31 to go that gave the Jackrabbits the lead for good at 53-52.
Western Illinois' Garret Covington was fouled on a 3-point attempt with 31 seconds left and he made all three free throws to get the Leathernecks within one, 60-59.
South Dakota State's Deondre Parks sank the first of two free throws and Mike Daum was fouled grabbing the offensive rebound. He made both free throws for a final score as Covington missed a 3-pointer.
Daum had 17 points and seven rebounds off the bench while Parks scored 16 points for the Jackrabbits (13-3, 2-0), who continued their best Division I start.
Covington scored 20 points and Tate Stensgaard 15 for the Leathernecks (7-6, 0-2), who led 32-27 at halftime.