Idaho (2-0) trailed 74-75 when Scott found Perrion Callandret for a 3-pointer with 56 seconds left.
South Dakota State's Skyler Flatten missed a 3 on the other end but, after grabbing the offensive rebound, Cody Larson missed a layup before Scott hit a 3-pointer coming out of a timeout to make it 80-75 with 10 seconds left.
Deondre Parks got a quick layup 2 seconds later and immediately fouled Scott, who hit a pair of free throws and closed the scoring at 82-77 with 6 seconds left.
Parks and Jake Bittle scored 18 apiece for South Dakota State (0-2). Larson finished with 14 points and 10 rebounds and Flatten scored 13.
Idaho made 8 of 15 from behind the arc and grabbed 16 offensive rebounds.