Oklahoma State (21-9) took a 2-0 lead in the fourth inning on Green's second home run of the baseball season, a two-run shot over the right-field wall.
The Cowboys extended their lead to 6-0 with a four-run eighth-inning outburst, keyed by Matt Hague's two-run single. Green also had a run-scoring single in the inning, while Neil Medchill added an RBI double.
Western Illinois (7-18) scored its only run in the ninth, as Cole Waddell's double scored Jared Wolf, who had doubled to start the inning.
Oklahoma State starter Matt Gardner (4-1) allowed four hits and no walks over eight innings. Starter Frank Zenisek (1-1) took the loss for the Leathernecks.