With the score tied 2-2 Weston scored a pair of runs in the top of the seventh and held off the hosts in their last turn to win it.
Krishna Lal had two hits for Weston and drove in two runs. Asher Lee-Tyson had two hits, including a double, and scored a run.
Tyler Hassett had 11 putouts at first base.
August Ratte pitched a complete game, striking out two and walking one.
Weston hosts New Fairfield for a rematch in the South-West Conference quarterfinals on Monday at 4 p.m.