Woodstown, now 21-8, will face Point Pleasant Beach, who holds an 18-6 record, in the state semifinal game on Monday.
Point Pleasant Beach advanced by defeating Shore 9-1 to claim the Central Jersey title.
The Wolverines took a 1-0 lead in the third inning following an RBI single from Thomas Tucci, and Chase Harding added a solo home run in the subsequent inning.
Rodriguez pitched the opening 2 2/3 innings, allowing two hits and three walks, while Hassler earned the victory by throwing the final 4 1/3 innings with six strikeouts.
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Maple Shade ended its campaign with a 16-10 record. The Wildcats were limited to three hits, with Edward Leahy collecting two and Chase Blum recording one.