Haugabook finished 30-for-43 passing with one interception for 297 yards, and 9-for-89 rushing for the Trojans (2-2, 1-0 Sun Belt).
The Ragin' Cajuns (0-4, 0-1) started ahead on an 80-yard run by Jason Chery 20 seconds into the game and a 6-yard run by Deon Wallace after Antwyne Zanders recovered a fumble on Troy's second play from scrimmage. They trailed only 21-17 at halftime.
Haugabook ran 15 yards and Cattouse 36 yards to tie the game at 14.
Drew Edmiston's 40-yard field goal gave the Cajuns their last lead, 17-14.
With 10:55 left in the half, Travis Boyd caught a 4-yard pass from Haugabook to make the score 21-17.
Cornelius Williams caught a 34-yard pass from Haugabook and Cattouse scored from nine yards out to boost the lead to 34-17 with 8:55 left in the third quarter.
The Cajuns got back within 10 points on a seven-play drive that took them 63 yards in 59 seconds. Mic Desormeaux passed twice to Richie Falgout for a total of 22 yards, then ran twice for 31 yards before Abdule Levier plowed in for a two-yard scoring run.
But Troy's Elbert Mack then intercepted a Desormeaux pass and returned the ball 39 yards for a touchdown with 5:23 remaining.
Desormeaux rushed 21 times for 159 yards, and got 158 yards passing, completing 20 of 38 with two interceptions.