CHICAGO -- Who needs home runs?

The Chicago Cubs scored on a single and double, tallied on a botched tag at the plate, a sacrifice fly had one run walked in and another come home on a hit batter in Tuesday's 6-3 victory over the Milwaukee Brewers.

For Chicago, there wasn't a long ball in sight in the opener of a three-game series.

"It doesn't really matter as long as we win," said Cubs first baseman Anthony Rizzo, who reached base four times and collected two RBIs. "We just want to keep finding ways to win."

The Cubs (63-48) moved to a season-high 15 games over .500 as they collected six runs over three early innings and ran their winning streak to five.

Right-handed starter Dan Haren (8-7) pitched 5 1/3 innings and earned his first victory as a Cub in his Wrigley Field debut.

He credits having former Diamondbacks and current teammate -- catcher Miguel Montero -- working behind the plate.

"It was definitely a sense of comfort for me having him back there," said Haren, acquired by Chicago on July 31 from Miami and making his second start. "He called a great game and the few mistakes I made were to (Brewers first baseman Adam) Lind.

"Overall, it definitely felt a little bit more comfortable out there than the first time."

Cubs left-hander James Russell pitched a scoreless ninth for his first save.

Brewers right-handed starter Taylor Jungmann (6-4) worked just 2 2/3 innings and threw 81 pitches in his shortest outing of the season as Milwaukee (48-66) dropped its third in four games.

"I think he struggled, he got behind quite a few hitters tonight," said Brewers manager Craig Counsell.

"It was lower 80 pitches in the middle of the third inning, so he struggled with his command tonight. He never could get it back and kept falling behind hitters."

Rizzo went 2-for-3 with two RBIs, was walked and also hit by a pitch for a major league-leading 23rd time as the Cubs picked up their 11th win in 12 games.

Chicago scored three runs in the second inning, one in the third and two more in the fourth to open a 6-1 lead.

Lind's two-run homer to right with none out in the sixth brought home left fielder Khris Davis, trimming the Chicago lead to 6-3.

Haren then struck out catcher Jonathan Lucroy, his final batter of the night. Haren worked 5 1/3 innings and gave up three runs on five hits while striking out six and walking just one.

Chicago's run of four straight games with first-inning runs came to an end after left fielder Kyle Schwarber's drive to the center-field warning track ended the frame. The Cubs, though, made up for it in the second with three runs.

Third baseman Kris Bryant doubled to right and came home on right fielder Jorge Soler's base hit up the middle. Soler scored from third on a one-out bunt by Haren after a toss from Jungmann was dropped by Lucroy. The Cubs proceeded to load the bases and center fielder Dexter Fowler's sacrifice fly to left drove in Montero with the third run.

Chicago made it 4-0 in the third when second baseman Chris Coghlan walked, stole second on an overturned call and came home on Rizzo's double to center with none out.

Jungmann departed with the bases loaded and two out, and Brewers right-hander Tyler Thornburg ended the threat when Russell ground to third. Jungmann worked 2 2/3 innings and gave up four runs (two earned), five hits and three walks while striking out three.

"I really have to make pitches and I didn't put myself in too many situations to make pitches," Jungmann said. "You can't make pitches on 2-0 counts, 3-0 counts. … I backed myself into corner in a lot of those situations."

The Brewers got one run back in the fourth as third baseman Elian Herrera doubled home Lind with two out. The Cubs replied in the bottom of the inning by loading the bases and scoring twice.

Thornburg walked Rizzo on four pitches to bring home Fowler for a 5-1 lead and with one out hit Soler with a pitch to plate Schwarber and make it 6-1. Thornburg gave up two runs, one hit, walked three and struck out two in 1 1/3 innings.

NOTES: The Brewers announced Tuesday that GM Doug Melvin would set down after 13 years as chief baseball executive. He'll eventually serve in an advisory role. ... The Brewers take a break from a stretch with 17 of 20 games at Miller Park for the three-game Cubs series at Wrigley Field this week. ... OF Ryan Braun sat out Tuesday's game. His next home run will be the 250th of his career, one behind all-time franchise leader Robin Yount. ... RHP Jimmy Nelson's streak of 25 2/3 innings without allowing an earned run -- snapped on Sunday -- was the fifth longest in Brewers history. ... RHP and ex-Cub Matt Garza (2011-13) takes the mound for the Brewers in Tuesday's middle game against Cubs RHP Jason Hammel (6-5, 3.17 ERA). ... Chicago starting pitchers were 8-0 during an 11-game stretch between July 29-Aug. 9, the most without a loss since May 20-June 2, 2001. ... CF Dexter Fowler saw a 22-game streak of reaching base safely snapped Sunday but still had a .415 on-base percentage and .440 slugging percentage during the span.