The Dodgers' Yasiel Puig unleashed a throw to the plate, but Hamilton beat it for game-winning tally.
Cesar Izturis went 3-for-5 with an RBI and J.J. Hoover (4-5) collected the victory for third-place Cincinnati, which clinched its three-game series and temporarily moved to within 1 1/2 games of National League Central-leading Pittsburgh.
Puig socked a two-run homer for NL West-leading Los Angeles, which dropped a third straight.
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