With time running out, the Bobcats (4-2) prepared to punt from their 33-yard line, but punter Ben Follis bobbled the snap and the Cowboys (3-2) took over at the Texas State 13 with 15.6 seconds left.
McNeese State's last chance ended when Cody Stroud, under heavy pressure, was called for intentional grounding with the clock running out.
Rutherford, who opened the scoring with a 22-yard run, completed 8 of 11 for 110 yards, and his scoring pass to Battle capped a 14-play, 79-yard drive that consumed 7:45.
Both teams came in with three-game winning streaks. Texas State, a former Southland Conference member like McNeese State, is an independent this season and in the process of moving up to the Football Bowl Subdivision.