With one out in the 10th, Adam Ottavino (0-1) hit Weeks with a pitch and, after the speedy infielder stole second, intentionally walked Ryan Braun followed by an unintentional walk to Aramis Ramirez that loaded the bases.
Lucroy followed with a fly to deep center, easily driving in the winning run for Milwaukee, which broke a four-year Opening Day losing streak.
Norichika Aoki hit a home run, Ramirez drove in a pair of runs and Jim Henderson (1-0) tossed a scoreless top of the 10th to earn the victory.
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