The Panthers finish one game out of the CAA playoff picture after Towson's 5-4 extra-inning victory over James Madison pushed the Tigers to 15 conference wins.
GSU finishes at 14-16 in CAA play and 24-31 overall despite its second extra-inning win in a regular season finale in as many seasons.
The Panther offense belted out 18 hits in the win, its second-highest total of the year. Senior Jonathan Kolowich also added a pair of hits, an RBI and a run scored.
Landon Anderson was hit by a pitch with the bases loaded in a tie game in the 12th to force in the go-ahead run before GSU added three more tallies.
Senior Jake Dyer (6-5) picked up his second win of the series by throwing 2.2 more scoreless innings, finishing with seven total shutout frames for the weekend.
Senior Justin Malone also pitched Saturday for the second time in the series and struck out two in 2.1 relief innings.
The Panthers got a strong start from freshman Jerry Stuckey, who struck out four and allowed just two runs over 5.1 innings.
"We came into today needing to win and we did absolutely everything in our power to get the job done," head coach Greg Frady said. "We left everything we had out there and did what we needed to do. I have a lot of respect for our seniors and what they've done for our program. Even though it's disappointing to see it end, winning the way we won today makes it feel a little better."
The Panthers started quickly, picking up three runs in the first inning against ODU starter Ben Tomchick.
After Caden Bailey and Williams each singled, Mark Hogan ripped a double into the left field corner to score both runners for a 2-0 Panther lead. Wood then scored Hogan with a single into center as GSU went up, 3-0.
Chris Baker's two-run triple in the third cut the Panther lead to 3-2, but GSU added a run in the seventh with an RBI single from Kolowich.
Aidan McLaughlin relieved Stuckey and stranded three ODU runners over the next two innings, including a first-and-third jam in the seventh to preserve the Panther lead.
After firing 122 pitches in Friday's game, the do-it-all senior Malone returned for one final outing. ODU wouldn't go down quietly, however, as Brandon Shelton's two-run single with two outs in the eighth tied the game.
Neither squad could score in the ninth, sending GSU to its fourth extra-inning game of the season.
With Dyer in the game and holding ODU scoreless, the Panthers finally broke through in the 12th. A pinch-hit single from Hogan started the inning, and GSU loaded the bases after a double by Kolowich and an intentional walk to Wood. Anderson was then hit, forcing in the go-ahead run. Kody Adams followed with a single into right that scored Kolowich as GSU went up, 6-4. Bailey then drove in the final two scores with a single into right field for a four-run advantage.
The Monarchs got a walk and a pair of singles in the bottom of the inning, but the Panthers tied up Josh Tutwiler on the bases between second and third after a two-out single for the game's final out.
GSU started and ended its conference season with extra-inning victories, posting a 13-12 walk-off finish over Northeastern back on March 16.
The Panthers will now miss just their second postseason appearance since starting CAA play in 2006, both having been decided on the season's final weekend.
Wood finished the series 7-for-13 with a team-high four RBIs and two runs scored.
Williams and Kolowich added four hits apiece against the Monarchs while senior Landon Bennett also added a base-knock.