Austin Evans returned an interception 16 yards for the Panthers' other touchdown.
Northern Iowa, No. 15 in the FCS Coaches Poll, had 417 yards total offense but only 11 first downs. The Panthers were 5 of 13 converting on third down.
South Dakota did not reach the end zone after a first quarter in which Kai Henry ran for a touchdown and Austin Simmons threw two touchdown passes for a 21-14 lead.
After Northern Iowa (4-3, 2-1 Missouri Valley) trailed 24-21 at halftime, McElvain and Weston connected on scoring passes of 65 and 54 yards in the third quarter. Hoosman's 1-yard run early in the fourth quarter closed out the scoring.
Weston had four catches for 189 yards. Hoosman carried 24 times for 111 yards.
Simmons completed 26 of 43 passes for 299 yards with the two touchdowns and three interceptions for the Coyotes (3-4, 2-1).
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