The Greeneville Astros held the Twins to two hits and posted a 2-1 victory Monday night at Pioneer Park.
Elizabethton, which had closed within a game of the Cardinals in the Appalachian League West Division, fell two games back with three to play.
Jonathan Matute's RBI single in the fifth inning broke a 1-1 tie, and the Astros bullpen held the Twins in check for th final five innings.
Greeneville had been eliminated from playoff contention a night earlier, but still managed to play an errorless game.
After Greeneville's Raymond Henderson's solo homer gave his team the lead in the first inning, Elizabethton's Amaurys Minier drove in a run with a groundout in the fourth to tie the game.
That was the last run the Twins would score.
Greeneville starter Guadalupe Chavez held Elizabethton to one hit over four innings. Reliever Ricardo Castro (3-2) earned the win with four effective inings.
Dariel Aquino pitched the ninth for his first save.