Combs converted a 3-point play with a layup and a foul, and Nick Osborne immediately followed with a 3-point shot as the Jaguars (6-12, 2-1 Summit League) took off on an 11-1 run, going from one point down, 49-48 into a 59-50 lead with 5:18 left in the game.
South Dakota State (13-4, 2-1) was unable to close in the final five minutes.
Mike Daum scored a career-high 23 points on 9-for-11 shooting. Deondre Parks and George Marshall scored 15 points each - Marshall with four assists - and Reed Tellinghuisen added 10 points before fouling out with 3:19 left.
The Jaguars took advantage of 21 South Dakota State fouls, sinking 21 of 25 foul shots.