MILWAUKEE -- The Milwaukee Brewers have been waiting all season for an offensive explosion like the one they produced Saturday night.

Three home runs, two doubles and more timely hitting than they've seen all season resulted in a season high for runs as the Brewers rolled to a 12-4 victory over the Chicago Cubs at Miller Park.

Brewers left fielder Khris Davis reached four times, scored three times and drove in three runs. Center fielder Gerardo Parra drove in three and added his first home run of the season.

Milwaukee right fielder Ryan Braun got into the act, too, walking twice and scoring two runs. Shortstop Jean Segura went 2-for-4 with a home run and infielder Jason Rogers hit the first home run of his career as Milwaukee collected 11 hits against six Cubs pitchers.

"We showed flashes of it in spring training," said Davis, who is 7-for-8 with three doubles, a home run and six RBI in his last two games. "Now that it is pulling up during the season it feels great."

The outburst was more than enough offense to overcome a short outing from right-hander Kyle Lohse (2-4), who lasted five innings while giving up four runs, seven hits and a walk with seven strikeouts but picked up his second victory of the season.

Cubs third baseman Kris Bryant hit the first home run of his career, a three-run shot to left field that wiped out a 2-0 Milwaukee lead in the third.

"It was nice just getting the first one out of the way, it's kind of been awhile," said Bryant, who returned to an empty dugout after rounding the bases. "But I did it. It's a cool feeling and we had fun with it.

"I know the type of player I am. I've always hit home runs in my life. So, just because I hadn't hit one in my whole time up here, I wasn't pressing at all. I was just trying to do my job to help the team win."

The Brewers answered by scoring three times in the bottom of the inning on a two-run double by Davis and a sac fly by Parra.

Cubs shortstop Starlin Castro cut the deficit to one with a run-scoring single in the fourth, but Segura answered with a leadoff home run in the bottom of the inning and the Brewers blew the game open an inning later.

After giving up six runs (four earned) through four innings, left-hander Travis Wood (2-2) had given way to Chicago's bullpen and there was trouble right off the bat.

Back-to-back walks to Braun and first baseman Adam Lind proved costly when Davis doubled for the second time, making it 7-4.

Another walk, this time to Parra, put runners at the corners with one out for catcher Martin Maldonado, who put the Brewers up four with a sacrifice fly to center.

"We just didn't get the pitching we needed tonight," Cubs manager Joe Maddon said.

Cubs left-hander Phil Coke got third baseman Elian Herrera to ground out before Rogers, pinch-hitting for Lohse, crushed a 2-1 fastball to center for his first career home run.

Milwaukee's bullpen took over from there, working four scoreless innings to preserve the victory.

"It's one game but we broke out offensively, which is a good thing," Counsell said. "A lot of guys had big nights offensively but to me, it's more that we have hitters starting to show signs of being the hitters they are, like Khris Davis. That's what's going to carry on longer than one win.

Catcher David Ross pitched a scoreless eighth inning for the Cubs.

NOTES: Brewers CF Carlos Gomez (left hip flexor) and 3B Aramis Ramirez (lower back tightness) sat out Saturday against the Cubs. It was Gomez's third straight game out of the lineup and the second in a row for Ramirez, who was scratched just before the game started Friday. ... The Brewers signed 3B Chris Nelson to a minor league contract and assigned him to Triple-A Colorado Springs. Nelson was released Friday by Philadelphia after he batted .278 with four doubles in 16 games for the Phillies' Triple-A affiliate. ... Cubs 2B Addison Russell extended his hitting streak to 12 games with a third-inning single. Russell has a hit in 14 of his 15 big league games in 2015.