Broadway passed for 316 yards and a touchdown and ran for 108 yards with a score for the Ragin' Cajuns (9-4), who repeated as New Orleans Bowl champions for the first time in school history.
Broadway went 21-of-32 through the air with an interception while Alonzo Harris led the Louisiana-Lafayette ground game with 117 yards and two touchdowns on 21 carries.
Jamal Robinson made six grabs for 116 yards.
Shane Carden picked up 278 passing yards with a pair of touchdowns and an interception on 25-for-42 efficiency for East Carolina (8-5).
Reggie Bullock led the Pirates' rushing corps with 99 yards and two scores on 16 carries.