Ranked 15th, Weston was tied with East Catholic 2-2 after one quarter and 6-6 at halftime before going up a goal in the third quarter.
Sean Fumai led Weston with four goals. He also had three assists.
Troy Flynn and Eli Page scored two goals apiece. Richie Miller (one assist) and Micah Zirn scored one each.
Peter Lummis added an assist.
Grant Limone had eight saves in goal for Weston, which faces sixth-ranked Morgan of Clinton in the semifinals on Wednesday at a time and location to be dtermined.