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.
Millions of Getty images now available for free via embed tool
Boston schools pull out free condoms over wrapping complaints