The right-handed duo combined for 12 strikeouts and retired 11 consecutive batters during one stretch. Farmer (9-4) allowed just two singles and struck out eight in six innings. He did not return after a lightning delay lasted 1 hour, 48 minutes in the seventh inning.
Roberts finished the game to pick up his second save despite allowing an unearned run in the ninth.
Brad Thomas and Mott Hyde each had two hits and drove in a run for Georgia Tech (35-26).
East Tennessee starter Kerry Doane (13-2) lost for the first time since March 16. After winning seven straight and earning the Atlantic Sun Conference Tournament title, the Buccaneers (36-24) mustered just two runs in two losses in their first regional since 1981.