The Jackrabbits improved to 6-2 overall. Arkansas, a College World Series qualifier a season ago, dropped to 8-3.
Arkansas gained a 1-0 lead in the bottom of the second inning with a two-out rally. Matt Vinson walked, stole second and scored on Collin Kuhn's base hit to left field.
SDSU took the lead in the fourth inning. Sawyer led off the inning by being hit by a pitch. Zach Rhodes followed with a single to move Sawyer to third and both runners scored on Eric Cain's double to center field.
Sawyer closed out the Jackrabbit scoring with a solo shot to lead off the sixth inning, his 23rd career home run in only 64 collegiate games.
Oberle, a junior college transfer from San Jose, Calif., held the Razorbacks to one run on three hits, while walking three and striking out three in 6 2/3 innings.
Vermeulen, the reigning Summit League Pitcher of the Week, allowed a run in the ninth on a sacrifice fly, but struck out leadoff hitter Jarrod McKinney with runners and second and third to end the game. Vermeulen struck out three in 2 1/3 innings to earn his first save of the season. He allowed one hit and issued a walk.
Rhodes and John Lee each collected two of the Jackrabbits' nine hits.
SDSU and Arkansas close out their two-game series at 3 p.m. Wednesday at Baum Stadium.
SOUTH DAKOTA STATE 3, ARKANSAS 2
SDSU 000 201 000 3-9-0
ARK 010 000 001 2-4-1
SDSU: Alex Oberle, Trever Vermeulen (7) and Zach Briggs. ARK: Sam Murphy, Jason Fuqua (4), Jeremy Heatley (8) and Monk Kreder, James McCann (5).
W-Oberle (1-0). L-Murphy (0-1). SV-Vermeulen (1).
HR: SDSU-Jesse Sawyer (4).