Lucroy, Carlos Gomez and Aramis Ramirez each homered off Yankees starter CC Sabathia.
Weeks' chopper skipped through the hole into left in the seventh off Alfredo Aceves (0-1), who was called for a balk two pitches earlier.
Rodriguez allowed two flyouts to the warning track in right in a scoreless ninth. The veteran closer hasn't allowed a run in 19 appearances this season.
Zach Duke (3-0) got the win after escaping a seventh-inning jam by getting Carlos Beltran to bounce into a double play.
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