Davies hit two-run homers in the first and fifth innings for the eighth-seeded Yellow Jackets (33-24). His second shot put Georgia Tech up 5-0.
James Ramsey had three hits for top-seeded Florida State (43-13).
His run-scoring sacrifice fly capped a three-run fifth, and his solo homer with two outs in the ninth made it a one-run game before reliever Alex Cruz got Jayce Boyd to fly out to end it.
Winning pitcher Buck Farmer (8-3) struck out six in six innings for Georgia Tech. Starter Scott Sitz (3-3) was charged with four runs allowed in 4 2-3 innings for the Seminoles.