The two had combined on Unicoi's first score an inning earlier when Powers hit a two-run double to score Vance and Grace Ann Clark.
Down by three in the final inning, Rylee Stiltner got things started with a single. A Greeneville error proved costly as Halie Padgett followed with a RBI single. Samantha Chavez, pinch hitting for Clark, then added a two-run double, followed by the back-to-back home runs.
"I thought that first hit boosted our team and gave us self-confidence," Vance said. "It gave us a lift and that's what we needed. Once we got some base hits, it just kept going from there. We started hitting."
The Lady Devils (37-9) will play at Elizabethton (25-13) in Wednesday's Region 1-AA championship game. Both teams have advanced to the sectional round.
Unicoi County appeared to be in real trouble after leaving the bases loaded in the top of the first and then giving up a three-run home run to Greeneville's Hanna Taylor in the bottom of the inning.
Katie Cronin then had a double in the second and single in the fifth inning and scored runs to add to the Greene Devils' lead.
Still, Unicoi County coach Grady Lingerfelt had confidence in his team entering those final two innings.
"It was probably the best comeback of the postseason," Lingerfelt said. "We had a lot of balls up in the air and straight at them. Then, a couple of balls fell in for us and we got going and got happy. The next thing you know…. The two runs we got in the inning before the final one was big to let us know we were still in it."
Padgett started before Allee Griffith came in the first inning and then went the rest of the game for the win.
Greeneville, which finished its season at 22-15, scored one run in the final frame when Brylee Jones' RBI single scored Kelci Cantrell. But, Stiltner ended the game by tagging Lilly Million in a run-down between second and third bases.