Bowling Green will play Tuesday night against Bonita, California.
Burwash struck out two batters and allowed only a walk during the sixth inning to preserve the win. He hit a leadoff double in the bottom of the fifth inning and scored the go-ahead run on Maddox Burr's infield single with two outs. Burwash also hit a leadoff home run in the first inning as Bowling Green built a 3-0 lead.
Taylors is the first South Carolina team to win a game at the series. Braden Golinski led the team with a two-run home run.
Bowling Green has won four straight elimination games since regionals.