McGuire extended Louisiana-Lafayette's 12-9 advantage with an 8-yard touchdown with 5:01 remaining in the game.
South Alabama went up 9-3 in the second quarter after Brandon Bridge connected with Jereme Jones for a 12-yard touchdown pass, but Louisiana-Lafayette responded with three unanswered field goals by Hunter Stover.
Terrence Broadway completed 16 of 28 passes for 216 yards and rushed for 54 yards on 11 carries for Louisiana-Lafayette (5-3, 4-0 Sun Belt). McGuire also caught nine passes for 90 yards.
Bridge was 16-of-27 passing for 177 yards for South Alabama and Shavarez Smith had eight receptions for 116 yards, including a 58-yarder.