The Cowboys swept the three-game series and improved to 27-14 overall and 8-7 in Big 12 play, while the Tigers, who entered the weekend in first place in the conference, fell to 27-9 and 8-4 in league action.
Corey Brown led off the seventh with an infield single and Adam Carr popped up to first, setting up Parrish's homer. He hit it to straight away center off of reliever Andrew Johnston (2-2) to give the Cowboys a 7-5 lead.
Justin Colbert, who went 4-for-5 on the day, hit a solo homer in the eighth to extend the advantage to 8-5.
Missouri jumped out to an early 3-0 lead in the first courtesy of James Boone's homer to left-center off of OSU starter Adam Daniels. Daniels lasted only 1.2 innings before being lifted for reliever Rick Rivas.
The Tigers touched Rivas for two runs in the third on RBI singles by Zane Taylor and Evan Frey to take a 5-0 lead.
The Pokes cut into the lead in the bottom of the inning with Parrish's first homer of the game, a three-run shot to left off of Missouri starter Doug Mathis.
OSU then tied the contest in the fourth on RBI singles by Corey Brown and Adam Carr.
Rivas (2-3) picked up the win with a solid relief outing, allowing two runs on five hits in 7.1 innings of work with three strikeouts and two walks. After giving up the two runs in the third he held the Tigers scoreless for the final six innings of the game.
Corey Brown had a career-best four hits on the afternoon and eight of the nine Cowboy starters chipped in with at least a hit each.
Oklahoma State will step out of league play for a Tuesday contest against Dallas Baptist at 6 p.m. before hosting No. 1 Texas (32-6, 9-5 Big 12) next weekend.
Parrish, Cowboys Complete Sweep of Tigers
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