Singles by Simunic and Yon Gomes gave the Vols runners on first and second with two outs, before Cody Brown's hard-hit grounder got by third baseman Ryan Peisel, allowing Simunic to score from second.
Gomes had three hits, including a two-run homer, to lead the Vols (14-7, 4-2 Southeastern Conference). Simunic had a run-scoring double in the seventh.
The victory went to Aaron Everett (2-2), who pitched a pair of scoreless innings with three strikeouts, ending Georgia's (12-8, 4-2) six-game winning streak.
McRee (2-1) took the loss, giving up one unearned run on two hits in 3.1 innings. He walked none and fanned three.
Bryce Massanari hit his fourth homer of the season for the Bulldogs in the seventh.