After a simple tweak, Wood cruised the rest of the way.
"It was a struggle there in the first," Wood said. "We weren't missing bad, but we were missing, so (there was) kind of a minor adjustment I had to make. I was kind of flying open a little bit there in the first after the first or second hitter, so we made it and were able to roll after that."
Wood (4-4) allowed two runs and struck out seven. All three of his walks came in the first inning.
"When he locates down into the corners, he's really, really effective," Chicago manager Rick Renteria said.
The Cubs won their first series since taking two of three against the St. Louis Cardinals from May 2-4.
"We had some timely hitting. Our pitching has been really good, and we've been able to close out the ballgames we lead," Renteria said.
Hector Rondon earned his fifth save in five chances after allowing a leadoff double to Ryan Braun in the ninth for Milwaukee's third hit. The Brewers, who began the day with the NL's best record, have scored 11 runs in five games.
"He keeps the fastball away well. He throws the cutter inside to right-handers well and mixes in a curveball," Brewers manager Ron Roenicke said about Wood. "He commanded the ball well, and we're a little bit off offensively. Three hits, just not many guys on base to do things with."
Marco Estrada (3-2) gave up four runs and seven hits -- five doubles and two homers -- in five innings. In nine games this season, Estrada has served up 12 home runs, second-most in the majors.
"I was terrible, plain and simple. Terrible," Estrada said. "I've got to figure things out. My off-speed pitches haven't been there and that's what's letting me down, that and elevating the fastball when I'm not trying to."
Castillo's two-run shot gave the Cubs a 2-0 lead in the second. Luis Valbuena scored on Castillo's fifth homer after drawing a walk.
The Cubs extended their lead to 3-0 in the third after Starlin Castro and Valbuena hit back-to-back doubles with two outs.
Olt hit his team-leading ninth homer in the fourth to make it 4-0. He leads NL rookies in home runs.
"I've just gotten some good pitches to hit," Olt said. "As long as I'm doing that, then I'm happy. The home runs, I guess, have come in bunches. Hopefully I can keep it going."
The Brewers had been scoreless for 20 straight innings, since the second inning on Friday.
"The first inning or two, when you have a pitcher in trouble, you need to get to them early," Roenicke said.