With the win, OSU stayed alive in the loser's bracket and will face either top-seeded Louisville or second-seeded Miami Sunday at 11 a.m. (CST).
Tyler Nurdin earned the win on the mound with seven solid innings, while the heart of the order, led by Tanner Krietemeier and Randy McCurry, did most of the offensive damage.
"I am proud of our guys for bouncing back today after a disappointing day (Friday vs. Miami)," said OSU head coach Josh Holliday. "We got a very good start on the mound and got some relief pitching late. We shut it down when they were making a run at us and did some good things offensively.
"Tanner's (Krietemeier) two-RBI single during the second inning to give us a 4-0 lead finally got us some breathing room for the first time in a while, and then Tyler's (Nurdin) ability to put up zeroes throughout innings two, three, four, five, and six and got that into the seventh inning."
After being shut out by Miami in the opening round Friday, OSU wasted no time getting on the scoreboard against the Falcons.
With two outs in the top of the first inning, Krietemeier drew a two-out walk, and following a wild pitch by BGSU's Cody Apthorpe, McCurry delivered an RBI single to give the Cowboys a 1-0 advantage.
OSU increased its lead in the second. Gage Green led off the inning with a triple, and a one-out single by Saulyer Saxon made it 2-0. A wild pitch allowed Saxon to advance two bases to third and after a walk, Donnie Walton stole second to put a pair of runners in scoring position.
And this time it would be Krietemeier coming up clutch, sending a single up the middle that brought home both runners and pushed the OSU lead to 4-0.
BGSU (24-31) collected its first run in the second, and the score would remain 4-1 until the seventh.
In that inning, the Cowboys added a pair of insurance runs. Jarrett Higgins led off the seventh with a double, and an RBI single by Walton made it 5-1. Walton then swiped his second base of the game, allowing him to later score on a McCurry two-out single.
OSU pushed its lead to 7-1 with an unearned run in the top of the eighth before the Falcons mounted their first serious threat in the bottom of the inning.
After giving up a bloop single and a four-pitch walk to open the BGSU eighth, Nurdin's day on the mound was done. Vince Wheeland came out of the Cowboys' bullpen and surrendered an RBI single to T.J. Losby to make it 7-2, then a throwing error by McCurry cut the OSU lead to four.
With BGSU runners on second and third and no outs, Wheeland struck out the next two hitters before a hit-by-pitch loaded the bases and brought the tying run to the plate. But Wheeland got pinch hitter Matthew Pitzulo to fly out to help OSU escape further damage.
Nurdin struck out five and allowed just two earned runs on seven hits as the southpaw improved to 5-3.
The Cowboys finished with nine hits, with Saxon and McCurry collecting two apiece, while both McCurry and Krietemeier picked up a game-high two RBIs.