Colby May, Peter Verdin, Levi Hyams and Matt Cerione also homered for the Bulldogs (32-8) who hit a season-high seven home runs. May had two hits and scored twice and Bryce Massanari also added a pair of hits.
Cecil Tanner (3-0) earned the win, allowing one run on three hits with five strikeouts in 3.0 innings.
"We got some good things going tonight and got some guys some much needed rest," Georgia coach David Perno said. "It was a good win for us because they are a good team that will probably win their division. It was nice to get the bats going tonight."
May blasted his 10th home run to straight away center in the first to put the Bulldogs ahead 1-0, then the Owls tied it in the second inning on an RBI single by Clint Roques.
Georgia took a 4-1 lead in the third after a leadoff home run by Verdin and a two-run blast by Poythress.
Poythress' second home run in the fifth made it 5-1, and Robbie O'Bryan's RBI double in the sixth extended the lead to 6-2. Kennesaw State (21-15) scored two runs in the seventh to cut the lead to 6-4, but Georgia got both runs back in the bottom of the inning.
The Owls struck for three runs in the top of the eighth to get within 8-7, then Hyams and Cerione hit back-to-back home runs for Georgia, and Poythress hit his third homer to right field two batters later to push the lead to 11-7.
Dean Weaver pitched the final 1.2 innings to earn his eighth save. Kyle Clayton (0-1) gave up four runs on seven hits in 2.0 innings to take the loss.
Eleven of Georgia's 13 hits were extra base hits including seven home runs and four doubles.
Georgia opens a four-game road trip Wednesday at Jacksonville State before heading to Ole Miss for a three-game series beginning Friday.