JSU won the opener 9-4 and held on for a 10-9 win in the second game.
The Gamecocks (29-22, 20-6 OVC) finished the game only a half-game behind Tennessee Tech in the league standings. Tech entered Saturday's play at 20-5. Belmont is 20-6 and tied with JSU in the standings.
In the opener, winning pitcher Casey Antley (5-4) scattered five hits and had seven strikeouts.
The Gamecocks jumped out to the lead after scoring three runs in the top of the first inning. Bishop led off with a single and Griff Gordon followed with a one-out single to left field. Coty Blanchard then doubled to right field to score Bishop. Paschal Petrongolo followed with an infield single to score Gordon and Andrew Bishop then singled up the middle to score Blanchard as JSU took a 3-0 lead.
JSU extended the lead in the fifth inning with a run and then added five runs in the seventh for a 9-0 lead.
Michael Bishop led the Gamecocks with his four hits, while Eddie Mora-Loera had three hits and Blanchard had a two doubles.
In the second game, Taylor Shields (7-2) scattered seven hits and gave up three earned runs to get the win. Stout pitched his way in the school record book by recording the final five outs to pick up his 16th save of the season, passing the old mark of 15 set by Todd Hornsby in 2011.
JSU had to hold on after leading 10-0 after three innings.
The Gamecocks are 9-1 in one-run games against OVC opponents and have won nine straight series against Eastern Kentucky. JSU has won seven of the last eight meetings between the two teams.
Blanchard finished with three hits and three RBIs.
Jacksonville State will be looking for the series sweep on Sunday as left-hander Tony Urban (3-1, 4.13 ERA) is scheduled to take the mound for the Gamecocks.