Southern Miss (37-23) has won nine of its past 11 under coach Corky Palmer, who announced in April that he's retiring after the season.
The Eagles can advance to the NCAA Super Regional with a victory on Sunday night against the winner of Sunday's elimination game between Georgia Tech and Elon.
Georgia Tech (36-18-1) committed a season-high five errors, including three by second baseman Connor Winn, that led to six unearned runs.
Luke Murton hit a three-run homer in Georgia Tech's four-run ninth. Thanks to the five errors, the Yellow Jackets trailed 10-3 before the inning.
Georgia Tech starting pitcher Brandon Cumpton (4-3), a former Greenbrier standout, gave up six hits and eight runs, only two earned, in 4 2-3 innings.
Tony Plagman drove in two runs for the Jackets.