The Ragin' Cajuns (3-3, 2-0 Sun Belt) had a season-high 528 yards of offense. Broadway was 14 of 21 for 225 yards, including a 62-yard pass to Elijah McGuire for the game's first score. McGuire added a 13-yard touchdown run in the third quarter.
Tyler Jones threw for 176 yards and a touchdown for Texas State (3-3, 1-1), which had just 94 yards rushing on 35 carries.
Will Johnson's 20-yard field goal trimmed the Cajuns' lead to 7-3 early in the second quarter, but Christian Ringo returned a fumble 41 yards for a touchdown and Alonzo Harris added a 1-yard score to help Louisiana-Lafayette to a 21-3 advantage at the break.
Louisiana-Lafayette finished with a season-high 288 yards rushing in its second straight win. Harris had 79 yards on 18 carries, and McGuire added 64 yards on the ground. McGuire also had four receptions for 85 yards.
Texas State trailed 34-3 before Jones threw a 33-yard touchdown pass to Brice Gunter with 1:04 left in the game.