Machado had reached base with a one-out single before moving to second on a wild pitch while Bellinger was at the plate.
Milwaukee manager Craig Counsell said: "I thought it was worth the risk of trying to expand to Bellinger, and if the at-bat goes to Grandal, we walk Grandal".
"We're in a good spot, man", Counsell said. "But I think a bunch of guys are not really on it right now offensively".
The most prominent struggler is Christian Yelich, the likely NL MVP from nearby Thousand Oaks.
The best-of-seven NLCS is now tied 2-2 with Game 5 on Wednesday afternoon at Dodger Stadium. However, he got roughed up in Game 1 of the NLCS by the Milwaukee Brewers, giving up five runs (four earned) on six hits in three-plus innings.
"It's a dirty play by a dirty player", Yelich said. "Eventually it's going to catch up to you". It was a great baseball game, it really was.
Muncy found a hole in the left side of the infield for a go-ahead RBI single that also kncked Woodruff out of the game. The Dodgers struggled to score two runs over 13 innings yesterday and I'm going to take advantage of a still-hot Milwaukee team in Game 5.
Davies wasn't on the roster for the NL Division Series.
While they haven't pounded the ball with the proficiency of Boston or Houston, the Brewers entered Game 4 of the NLCS leading the playoffs with a.265 team batting average.
But Milwaukee lost for just the second time in its last 15 games because the Brewers didn't generate almost enough offence to back their pitching staff, which turned in another stellar night of work.
Ryan Braun contributed three singles in Game 4, but the rest of the lineup was dire.
"Exhausting", Los Angeles outfielder Chris Taylor said.
Domingo Santana later tied the score for the Brewers with an RBI double in the top of the fifth frame. Jesus Aguilar went 1-for-5 with a walk. Manny Pina finished 1-for-2 with a double and two walks. Orlando Arcia was 1-for-5 and scored the lone run.
Dodgers reliever Julio Urias (1-0) pitched a scoreless 13th inning to earn the victory.
The Dodgers didn't necessarily need a home run to get them out of their rut - they just needed to get someone on base and maybe, just maybe, they could find a way to advance him home.