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Nadal, Murray reach U.S. Open semis
Mike Napoli hit a sacrifice fly for one run for the Angels and Robb Quinlan had the other RBI.
Weaver had a no-hitter through four frames and allowed just the one hit over seven innings. He struck out six and walked two.
But it was Shields (2-0) who got the win, the Angels' second straight.
Chicago starter John Danks scattered seven hits in 6 1/3 innings. Octavio Dotel (1-2) took the loss.
Carlos Quentin, A.J. Pierzynski and Joe Crede had Chicago's three hits.
