NL Central-leading Chicago had gone scoreless for 17 straight innings before breaking through against Hader, who hadn't allowed a homer all season long.
''I think that's extremely rewarding as a group and gives you a lot of momentum,'' Cubs manager David Ross said. ''(There's) a lot of positivity, especially going forward, if we want to continue on the championship path that we want to be on.''
Javier Baez and pinch-hitter Anthony Rizzo sparked the rally with consecutive one-out singles. Heyward then put the Cubs ahead to stay with a deep drive to center for his sixth homer.
''I was trying to go inside,'' Hader said. ''Obviously I'm not too sure where it went, but I'm going to assume it was probably down and in. Probably a good pitch for him to just drop the barrel on.''
Lefties were batting just .115 with six homers against Hader in the All-Star closer's career coming into the game. He hadn't allowed a hit to a lefty all season long before Saturday.
''Balls down the middle are going to get hit, no matter who you are out there,'' Brewers manager Craig Counsell said. ''You don't get a pass for those pitches.''
After Heyward and company returned to the dugout, Ildemaro Vargas followed with another homer to give Chicago a 4-2 lead. Hader (1-2) then retired the next two batters, but the damage was done.
''These kind of things carry into other games,'' Ross said. ''Where once you've done it, once you've come back, once you've faced one of the best in the game and beat them at the back end when things weren't going well throughout the day.''
Milwaukee wasted a strong effort by Brent Suter, who stepped in after Brett Anderson was scratched because of right hip soreness. Suter struck out six in three scoreless innings, and four relievers combined for five innings of three-hit ball before Hader faltered in the ninth.
''For eight innings, we pitched very very well,'' Counsell said. ''Brent did a heck of a job getting us through three innings. ... It went as good as we could have hoped and put ourselves in a good position. It just didn't work out in the end.''
Ryan Braun hit a two-run homer for the Brewers, who posted shutout wins in their previous two games. Avisail Garcia, Keston Hiura and Dan Vogelbach had two hits apiece.
Jason Adams (1-1) got one out for the win, striking out Christian Yelich with a runner on first to end the eighth. Craig Kimbrel earned his second save, continuing his turnaround after a rough start to the season.
Hiura and Jedd Gyorko opened the ninth with consecutive singles off Kimbrel. But Vogelbach struck out swinging, Ben Gamel bounced into a forceout and Orlando Arcia lined out to end the game.
While Chicago struggled at the plate for most of the night, Kyle Hendricks kept the Cubs in the game with 7 2/3 solid innings. The right-hander allowed six hits, struck out seven and walked none.
SUTER THE GYMNAST
Suter even threw in a bit of gymnastics in the third. On a 1-0 pitch to Ian Happ, Suter lost his balance and did a perfect somersault off the mound. Cheers came out of the Brewers dugout as he regained his composure and struck out Happ.
Cubs: OF Cameron Maybin was scratched due to a stomach illness.
Brewers: The 32-year-old Anderson is day to day. Manager Craig Counsell said he should be ready at some point during the team's five-game series against St. Louis that begins on Monday.
RHP Alec Mills (4-3, 4.74 ERA) starts for Chicago for Sunday, RHP Adrian Houser (1-4, 5.48 ERA) pitches for the Brewers.
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