Brent Suter (2-1) pitched two scoreless innings in relief of Freddy Peralta, helping Milwaukee to its fourth win in five games. Josh Hader got three outs for his fourth save in four opportunities, working around a leadoff walk.
Keston Hiura had three hits and Kolten Wong finished with two as the Brewers bounced back from a 15-2 loss in the series opener Friday.
''Yesterday had already passed and we came here this morning to keep fighting,'' Pina said.
Cubs manager David Ross was ejected by plate umpire Corey Blaser in the ninth following a strike one call on Jake Marisnick with a runner on first and none out. Marisnick struck out on three pitches.
''That looked extremely high,'' Ross said. ''That was a bad call. I mean, plain and simple.''
Jason Heyward homered for Chicago, which had won four in a row. Eric Sogard had three hits.
The Cubs jumped in front on Nico Hoerner's two-run double in the second. After a shaky start, Adbert Alzolay retired 12 in a row.
Hiura broke up Alzolay's streak with a leadoff double in the fifth. Making his major league debut in his hometown of Chicago, pinch-hitter Corey Ray walked with two out to put runners on the corners.
Ross then brought in left-hander Rex Brothers, who walked Wong and Omar Narvaez to force in a run. Brothers also hit Tyrone Taylor in the foot to force in another run, tying it at 2.
Milwaukee manager Craig Counsell credited Ray's walk for sparking the rally.
''The biggest part, we got Brothers in the game,'' he said. ''That was probably earlier than they wanted and it turned the game for us.''
Pina's blast with one out in the seventh off Andrew Chafin (0-1) put the Brewers on top. Pina's second homer of the season and third career pinch homer drove in Wong, who led off with a single.
''Sometimes the manager doesn't want to use the backup catcher in that situation,'' Pina said. ''But that was good for him today to think Manny was the right guy to change the game.''
Heyward went deep against Devin Williams with two out in the eighth.
The last time Brandon Woodruff faced the Cubs on April 13, Chicago's Ryan Tepera admitted he threw behind Woodruff as retaliation for the right-hander hitting Willson Contreras earlier in the game.
Woodruff faces the Cubs again in the finale of the three-game series, but said Saturday he's not thinking about the incident.
''I knew the questions would come, but I've put it behind me,'' he said. ''I'm focused on going out and competing and doing my job.''
Ray was with the Brewers but didn't find out he was being activated until just before first pitch. His father made his way to Wrigley Field (about a 30- to 40-minute trip) as soon as he found out.
''I didn't start, so that gave him a lot of time,'' Ray said.
The Brewers placed pitchers Brett Anderson (right leg) and Josh Lindblom (right knee) on the 10-day injured list and recalled Ray and right-hander Phil Bickford from the team's alternate site.
The Cubs optioned left-hander Kyle Ryan to their alternate site to make room for Alzolay.
Brewers: OF Christian Yelich (lower back) was eligible to be activated from the 10-day injured list on Saturday, but instead was sent back to Milwaukee for an MRI. ''Nothing happened yesterday,'' Counsell said. ''We're just at a plateau, and so we're just trying to rule everything out and see if we can get any new ... piece of information.''
Woodruff (1-0, 1.96 ERA) faces the Cubs for the third time this season. The righty has two no-decisions in the previous starts, allowing one run in 13 innings. Right-hander Jake Arrieta (3-1, 2.86 ERA) pitches for Chicago on Sunday.
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