In the second inning Hyams smashed a three-run home run just inside the right field foul pole to give Georgia a 3-0 lead. Chase Davidson singled with one out, then a fielding error by Alabama put runners on first and second before Hyams' first career home run.
Alabama (11-4, 2-0 SEC) sent nine batters to the plate and scored four unearned runs to take a 4-3 lead in the third.
A lineout double play ended Georgia's scoring threat in the top of the fifth, and the Crimson Tide's right fielder Kent Matthes hit his NCAA-leading 12th home run in the bottom of the fifth to push the lead to 5-3.
Three more Alabama runs in the bottom of the sixth made it 8-3, and the Tide added one more in the eighth before Georgia scored two runs in the ninth.
Trevor Holder (3-1) worked five innings and gave up five runs, only one earned, on five hits to take his first loss in his last seven starts dating back to last season.
Austin Hyatt (4-0) allowed three runs on eight hits in eight innings to pick up the win.
In game two, the Crimson Tide jumped on Georgia with a grand slam in the first before the Bulldogs answered with a three-run home run by Joey Lewis in the third.
The Bulldogs threatened again in the fifth as Hyams led off with a double, Taylor walked, and a sacrifice bunt by Demperio moved runners to second and third, but Colby May's rocket was caught by the Alabama third baseman, who stepped on third for the double play.
The Tide began to pull away with four runs in the fifth off four hits and two Georgia errors. A pair of home runs in the seventh by Cody Trotter and Taylor Dugas made it 11-3.
Georgia scored single runs in the eighth and ninth for the final margin.
Poythress had two hits, and Peter Verdin came off the bench to add a pair of hits for Georgia.
Justin Grimm (1-1) surrendered seven earned runs on seven hits in four innings to take the loss. Adam Morgan (3-0) worked 7.1 innings and allowed four earned runs on eight hits to earn the win for Alabama.