McNeese State starter Rusty Begnaud ran his record to 3-0 after going seven innings and giving up one run on five hits while striking out five.
Arkansas dropped to 8-5 overall and has now lost two straight, while McNeese State improved to 9-5 with the win. The weekend series loss is the first to a non-conference opponent at home for the Razorbacks since being swept by Long Beach State in 2000.
The Cowboys jumped out to a 2-0 advantage in the first inning on Tommy Eubanks' two-run home run to right.
The Razorbacks cut the lead to 2-1 in the sixth inning on an RBI single to center by Clay Goodwin that scored Kirk McConnell.
McNeese State increased its lead to 4-1 in the seventh inning on an RBI single by Tim Lemke that plated Ran Prince and Josh Fontenot.
The Razorbacks tried to mount a rally in the eighth when Andrew Wishy and Clay Goodwin each walked with one out in the inning. But, McNeese State relief pitcher Jared Gothreaux forced Nick Pitts to hit into a fielder's choice and then got Jeff Fletcher to ground out to end the scoring threat.
The Razorbacks and Cowboys each stranded nine runners on base in the game and each hit three batters.
The Razorbacks now travel to Norman for a Tuesday meeting against the Oklahoma Sooners. Game time is set for 3 p.m. The Arkansas Baseball Network will go on the air at 2:40 p.m.