Chicago, the division champ two years running, has spent all of three days in first place this season. The Cubs were tied after winning their season opener on March 29, then fell as far as fourth before taking a half-game lead with a victory over Colorado on April 30.
They fell out of first place two days later and have been chasing Milwaukee ever since.
"We always want to win," Cubs manager Joe Maddon said. "We want to be in first place, but we want to be in first place at the end of the year. Getting there now is always nice."
The Cubs moved into first thanks to a five-run 11th and an eighth-inning rally against Josh Hader. Anthony Rizzo started the 11th with a homer off Matt Albers after Jason Heyward hit the game-tying single in the eighth.
Rizzo's homer gave him an RBI in eight straight games, lifted the Cubs to their seventh straight win over Milwaukee and 13th win in 17 games overall.
It will be up to right-hander Tyler Chatwood to keep the momentum going but he'll need to find a way to reduce his walks.
Chatwood has issued 56 free passes in 58.1 innings this season and has walked at least five batters in eight of his 12 starts.
The right-hander last pitched Thursday afternoon in a 4-3 win over the Philadelphia Phillies when he allowed a run in 4 2/3 innings but matched a season-high by issuing seven walks.
"Today is the best I felt in a while," he said. "Obviously the results weren't there. Physically I felt good. I felt like the ball was coming out (good) for the most part. Obviously, I walked way too many guys, but it's a step in the right direction even though it didn't look like it."
Chatwood is 3-1 with a 3.00 ERA in four career starts against Milwaukee. He last faced the Brewers April 29 at Wrigley Field when he allowed two hits in seven innings in a 2-0 win.
Milwaukee held a 4 1/2 game lead over the Cubs less than two weeks ago, but has gone 3-6 since, dropping two of three to the White Sox, and a pair at Cleveland before rebounding with two victories in three tries at Philadelphia over the weekend.
The Cubs though have been rolling during that same stretch and as a result, the Brewers will wake up Tuesday morning looking up in the standings for the first time since May 17.
They might have been able to whether that storm if not for an abysmal showing this season against the Cubs, who've won eight of the first nine meetings.
"You have to be pretty darn good against teams like this," Brewers manager Craig Counsell said."
It will be up to Chase Anderson to keep the surging Cubs in check. The right-hander took the loss his last time out, allowing three runs on four hits over 4 1/3 innings against the Indians, and is 0-2 with a 7.24 ERA over his last three starts.
Anderson is 3-4 with a 3.33 ERA in nine career starts against the Cubs and has done well against them this season, posting a 2.08 ERA in two starts but the Brewers' offense has been unable to give him any support in those outings.