The 20th-ranked Panthers (8-4) scored on their first nine possessions as they posted the largest margin of victory in a FCS playoff game in school history.
UNI's biggest previous margin of victory in the playoffs was its 36-point win over Eastern Illinois in 2015 (53-17). The Panthers advance to play South Dakota State (9-2) next Saturday in Brookings S.D., with a 2 p.m. kickoff.
Eli Dunne passed for 260 yards and four touchdowns, while Daurice Fountain hauled in 10 passes for 139 yards and two scores.
Defensively, UNI picked off Monmouth quarterback Kenji Bahar four times, two by Nikohl Jaghai, and one each by Xavior Williams and Elijah Campbell.