East Carolina (8-5) also had trouble containing dual threat Cajuns quarterback Terrance Broadway, named the game's most valuable player after passing for 316 yards and rushing for 108.
Alonzo Harris rushed for 120 yards, including touchdowns of 6 and 68 yards for the Ragin' Cajuns (9-4), who briefly squandered a three-touchdown lead before moving back in front for good on Broadway's 14-yard scoring pass to Javone Lawson late in the third quarter.
"Nothing fazes our team," said Broadway, who also ran for a 12-yard score. "Everybody on our team responds to adversity well. So when they came back on us and made a game out of it, our team is still upbeat and saying we're going to win this game."
And they did, with Brett Baer adding his second and third field goals in the fourth quarter to seal the victory.
Carden passed for 278 yards and two touchdowns, but was also plagued by a couple of receiver drops on long passes.
"They did a good job of changing, I guess, the coverage throughout the game," Carden said of ULL. "But I think our offense could execute a lot better. It was nothing really they were doing. It was a lot of us just not executing routine plays."
The Pirates' Reggie Bullock rushed for 104 yards and two touchdowns.
Storylines Defending their bowl title
O Quarterback Terrance Broadway throws for 316 yards and rushes for 108 to lead Louisiana-Lafayette to its second straight win in the New Orleans Bowl.