Coprich ran for 251 yards and four touchdowns and Roberson ran for 121 yards and a TD as the Redbirds (9-2, 7-1 MVFC) earned a share of their second straight Missouri Valley Football Conference championship.
Illinois State shares the crown with four-time defending FCS champion North Dakota State.
Leading just 3-0 after a quarter with a snowy gale blowing at their backs, the Redbirds scored 20 points into the wind in the second quarter and never looked back.
''It was not how we drew it up, we hoped to do it in the first quarter, but it worked out.'' Illinois State coach Brock Spack said.
Coprich had 122 yards and two scores in the first half as the Redbirds took a 23-0 lead into halftime. Coprich's TD runs covered 12, 12, 45 and 74 yards.
Roberson completed just two passes in the game, but one was a 20-yard TD to Christian Gibbs with 2:49 left in the half to go up 16-0. He scored on n 80-yard run in the second half.
''They did a real nice jobs on us,'' South Dakota coach Joe Glenn said. ''I'm kinda disappointed in those real long runs. They had lots to play for, a championship and all that stuff. I'm just a little disappointed in our finish today. I didn't think that was us.''
South Dakota struggled early in the snow and into the driving wind. Miles Bergner's first punt went minus-6 yards and the second 8, giving the Redbirds a field position advantage.
Sean Slattery's 33-yard field goal with 2:51 left in the first quarter gave ISU a 3-0 lead.
Illinois State's drove 50 yards to go up 9-0 on Coprich's 12-yard TD run. Coprich gained 48 yards on the drive that ended with a bobbled snap on the PAT.
Roberson's pass to Gibbs was followed by Coprich's 45-yard score just before half. He added a 74-yard run for a score early in the second half.
USD (5-6, 3-5) had the wind in the third quarter, but the Coyotes' Paul Anderson fumbled the second-half kickoff and the Redbirds recovered on the USD 25. Four plays later, Coprich scored again on a 12-yard run.
USD was held to just 155 total yards.
Ryan Saeger was 3-for-19 passing for 24 yards.
Drew Potter carried 15 times for 76 yards.
The Coyotes were denied their first winning season since 2011.
''You just hate ending on a sour note,'' Glenn said. ''This is a good football team. I don't think they're that much better than us.''