The Astros then held on for a 7-4 victory, keeping the K-Mets a game and a half behind Appalachian League West Division leader Elizabethton after the Twins dropped an 8-7 decision to Princeton on Tuesday.
Kingsport entered the fourth inning leading 2-0, but that changed in hurry.
K-Mets starter Andrew Church (3-5) was tagged for five runs — three earned — during an inning that featured four hits, two errors and a walk. The big blow in the frame was a two-run homer by Greeneville's Bryan Muniz, his second of the season.
Kingsport (31-28) battled back by plating a pair of runs in the fifth on a two-run double by Zach Mathieu, but that was all the offense the K-Mets could muster. Mathieu, Vicente Lupo and Luis Ortega had two hits each for Kingsport, which had nine hits as a team.
Reliever Zach Davis (2-0) earned the victory for Greeneville (29-28), throwing three innings of shutout ball while allowing just one hit and striking out four batters. Eric Peterson pitched the ninth to earn his fifth save of the season.
The K-Mets will be off tonight before starting a three-game series on the road against the Bluefield Blue Jays on Friday.