The Rebels pushed three runs across in the second, six in the third and three in the fourth to stake a 12-0 lead. ULM held them scoreless over the fifth, sixth and seventh innings before a bases loaded walk and an error pushed across two more runs in the eighth.
David Phillips, who finished the game 2-for-2 with three RBIs, homered in the second and Matt Smith and Matt Synder hit back-to-back homers in the third to pace Ole Miss' (1-1) offensive attack.
Barrett (1-0) yielded just a pair of hits and struck out seven Warhawk batters over six innings of scoreless work to pick up the victory for the Rebels. He combined with Eric Callender to hand the Warhawks their first shutout loss since 2007.
Luke Briley pitched well for the Warhawks out of the bullpen not allowing a hit over 1.1 innings of work before handing the ball off to John McDermid to pitch the eighth inning.
Nick Wade led ULM at the plate going 2-for-4 on the afternoon. Perry Smith and Kelvin York each had one hit for the Warhawks as they lost for just the second time in their last five games against a Southeastern Conference opponent.
Josh Miller (0-1) was tagged with the loss for the Warhawks (1-1) after he was charged with eight runs on six hits over 2.1 innings of work. He finished with three strikeouts and a pair of walks.
The teams will play the rubber game of the series Sunday afternoon at 1:30 p.m. The Warhawks will send senior right-hander Corey Brown the bump and the Rebels will counter with junior right-hander Trent Rothlin.
The game will be broadcast live in northeast Louisiana on 540 AM and worldwide on the internet at ulmwarhawks.com.