Yamamoto gave up just one run on three hits, while striking out six and walking one batter on 111 pitches.
He became just the 13th pitcher in MLB Postseason history to throw a complete game in the NLCS. His complete game is the first one in eight years for both leagues - Justin Verlander in Game 2 of the 2017 ALCS.
It was also Yamamoto's first complete game as a member of the Dodgers.
Milwaukee's young star Jackson Chourio scored the team's only run of the game with a solo home run in the first inning.
From then on, it was all Dodgers.
LA took the lead in the second inning, starting off with a solo home run from Teoscar Hernandez to deep left field, becoming the Dodgers' all-time postseason leader with 14.
It was Hernandez's fourth of the postseason and a make-up for getting called out at the plate in last night's crazy double-play moment.
In the same inning, Andy Pages hit a double down the right field line to score teammate Keke Hernandez from second.
It was Pages' first hit of the series and his second hit of the postseason (2-for-28).
Max Muncy, who was robbed of a grand slam in Game 1 of the series, got his revenge this time around and sent one to deep center off starting pitcher Freddy Peralta. And this time around, he hit it where Sal Frelick couldn't catch it.
Peralta's day was done after giving up the home run. He finished after 5.2 innings of work, giving up three runs on five hits with five strikeouts and one walk.
Aaron Ashby came in for Abner Uribe in the seventh inning after the latter recorded an out and gave up a double to Keke Hernandez.
Shohei Ohtani would single off Ashby to bring in Hernandez from third, who moved over on a sac-bunt from Pages, to put the Dodgers up 4-1 before eventually stealing second base himself.
It was Ohtani's first hit and first RBI of the NLCS.
Dodgers' Tommy Edman added on a little extra insurance in the top of the eighth inning to bring home Will Smith for the 5-1 lead.
Milwaukee couldn't find a way to rally back, finishing the game without a single baserunner in scoring position on a total of three hits. Meanwhile, the Dodgers finished 2-for-11.
Now, the Brewers are in a major hole as the series goes back to Los Angeles for Game 3 on Thursday, October 16th.
LA is two wins away from returning to the World Series.
