Rylan Thomas hit a three-run home run to cap off the frame, which began with a pair of ground outs. Trailing 2-0 with two outs, the Reds batted through their lineup before the inning ended with a ground out by Justin Bellinger.
The Appalachian League West Division-leading Twins fell to 27-21, while the Reds improved to 20-30.
The big seventh inning meant a no decision for Elizabethton starter Josh Winder, who threw five scoreless innings and gave up just two hits and no walks.
Reliever J.T. Perez suffered the loss, giving up four runs over 1 2/3 innings. Zach Neff was cited with giving up five runs in 1/3 inning.
Elizabethton took the early lead when Gilberto Celestino tripled on a line drive to left field to drive in Yunior Severino for the Twins’ first score in the top of the first. They increased the lead to 2-0 in the top of the fourth with a RBI double by Alex Robles to drive in Chris Williams.
The Twins wouldn’t score again until a three-run home run by designated hitter Colton Burns in the ninth inning. Williams went 2-for-3 with two runs scored and Robles was 2-for-4 with a pair of doubles.
Lead-off Mike Siani and Reniel Ozuna each had two hits to lead Greeneville. Lyon Richardson pitched the first 3 2/3 innings for the Reds. Eduardo Salazar (1-0) earned the win, giving up three hits and three runs over 5 1/3 innings.
The teams are scheduled to play the second game of a three-game series Monday night at 7.