Oliver returned the favor with 25 minutes left, setting up Joseph for a 35-yard goal that made it 2-0.
OHS then scored three goals in six minutes, the first by Theo Malone, the second by Peter Paluch and the third by Paul Bischoff.
“We needed some boys to step up tonight and they did,” said OHS coach Alex Brannan, whose Yellowjackets avenged a 4-3 overtime loss to defending Section Four Class B champion Susquehanna Valley (9-1-2, 9-1-2) earlier this season. “I’m sure (SV) will remember this.”
Jeremy Leary made three saves in the shutout for OHS.
Oneonta (9-2, 9-2), which also fell to SV in the 2012 sectional final, visits Seton Catholic Central on Monday.
Hamilton 2, Cooperstown 1
Pat Salmon scored early in the first overtime as Hamilton earned a Center State Conference victory on the road, despite being outshot, 13-7.
Salmon’s winner came on a 25-yard that dipped below the cross bar as the team’s played overtime in a downpour.
Cooperstown (7-4, 6-3) took a 1-0 lead on a goal by Jordan Manikus with 19:09 left in the first half. Manikas beat two defenders near the left baseline before beating Lucas Ord to the near post.
“The first half, when we scored, we went into a defensive posture,” Cooperstown coach Frank Miosek said. “We had a hard time getting them to push up. We looked like we didn’t want any part of playing offense. In the second half, we beat them to 50-50s and had some good crosses.”
Cooperstown outshot the Emerald Knights, 10-2, in the second half.
“We dominated the second half,” Miosek said. “We hit the cross bar twice and the far post once.”
Dakota Thomas tied the score at 1 4:48 before halftime. Salmom one-touched a pass to Thomas, who finished from 6 yards for Hamilton, which improved to 8-2-1 overall and 8-0 in the CSC.
Cooperstown will play Owen D. Young on Tuesday.