The Wildcats (9-3, 7-1) entered the game tied atop the conference standings with Montana and Sacramento State, which beat UC Davis while the Grizzlies lost to Montana State on Saturday.
Weber State finished the regular season undefeated at home for the second straight year, and has beaten Idaho State (3-9, 2-6) in 16 of the last 17 meetings.
Constantine was 16 of 23 for 289 yards passing, David Ames caught four passes for 140 yards and a touchdown. Devon Cooley had two TD catches and Ty MacPherson had one. Josh Davis added 88 yards rushing on 12 carries that included a 24-yard run.
David Allish kicked a 45-yard field goal in the third quarter for Idaho State (3-9, 2-6). Sagan Gronauer threw a 49-yard touchdown pass to Michael Dean with about two minutes left.
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