Broadway tossed a 5-yard touchdown pass to Jared Johnson late in the first quarter to give the Ragin' Cajuns (6-3, 5-0 Sun Belt) a 7-3 lead and McGuire and Effrem Reed each punched in short runs to make it a 21-3 lead at halftime.
Broadway threw 4 yards to McGuire in the third quarter and again to Johnson in the fourth to make it a 37-9 advantage.
McGuire finished with 135 yards on 26 carries to lead a Louisiana-Lafayette rushing attack that garnered 244 yards on 54 carries.
Broadway finished 12 of 23 for 158 yards as Louisiana-Lafayette held almost a 13-minute advantage in time of possession.
Tyler Rogers was 20 of 35 for 206 yards to lead New Mexico State (2-8, 1-5).