Suarez went 3 for 3 and drove in three runs, taking another step forward after slumping for much of the season. Winker had two hits and scored twice.
The Reds scored exactly six runs for the third straight game after scoring a total of six runs during a four-game slide.
''All of our hitters continue to work and look for adjustments,'' manager David Bell said. ''It's nice to see the hard work pay off with results. It couldn't come at a better time - right when we need it.''
Mahle (1-1) shook off a slow start on his way to 11 strikeouts over 6 2/3 innings. The right-hander pitched shutout ball after surrendering solo drives by Anthony Rizzo and Kyle Schwarber in the first.
''Solo home runs make you feel like you're still in the game,'' said Mahle, who fell one strikeout short of matching his career high. ''We just kind of kept going and found our groove.''
NL Central-leading Chicago dropped its third consecutive game. Willson Contreras and Jason Heyward homered in the ninth, but Raisel Iglesias got two outs for his fourth save.
Cincinnati went ahead to stay with two runs in the fourth. Winker hit a tying drive for his ninth homer, and Matt Davidson made it 3-2 with an RBI single against Kyle Hendricks (3-4).
''Looked like he couldn't get the changeup down a little bit a couple times tonight.'' Chicago manager David Ross said. ''They did a good job of beating some shifts.''
Suarez added a bloop two-run single with two out in the fifth, and Freddy Galvis hit an opposite-field drive to right on Kyle Ryan's first pitch of the eighth for his sixth homer.
''When I saw that bloop, I said, 'That's all I needed,''' Suarez said. ''I didn't need another home run - just drive in those guys and hurt the other team.''
Hendricks allowed five runs and a season-high 10 hits in six innings. The right-hander also lost at Cincinnati on July 29, surrendering six runs in 4 1/3 innings.
''Physically, I felt fine,'' Hendricks said. ''Just disappointing. Just not in a good spot right now, just making enough good pitches. Over the last few games, everything has felt pretty good, I'm making some bad pitches. Same thing today. Some balls found holes, but just too many hits in general, too many bad pitches, hard contact.''
Rizzo hit Mahle's second pitch of the game deep into the right-field seats for his sixth homer of the season. It was his 19th at Great American Ball Park and No. 29 overall against the Reds, two more than he has against any other team.
Schwarber, who grew up about 25 miles north of Cincinnati in Middletown, added an opposite-field shot to left for his seventh homer of the season and ninth of his career in Cincinnati.
Suarez led off the second with his seventh homer, a fly ball that barely cleared the fence in left. He has homered in two straight games.
LAURA ON HAND
The remnants of Hurricane Laura showed up in the middle of the game in the form of a persistent rain that lasted the rest of the way.
The Reds reinstated right-hander Anthony DeSclafani from the paternity list. They also designated outfielder Phillip Ervin for assignment and recalled right-hander Jose De Leon from their alternate training site.
The Reds acquired right-hander Riley O'Brien in a trade with Tampa Bay for left-hander Cody Reed, who was designated for assignment Monday. O'Brien, 25, was sent to the team's alternate training site.
Cubs: RHP Dan Winker was hit by a comebacker off the bat of Nick Castellanos in the seventh, but the reliever stayed in the game after a brief visit from a trainer.
Reds: LHP Wade Miley was placed on the 10-day injured list with a left shoulder strain.
Cubs: RHP Yu Darvish (5-1) goes for his sixth consecutive win in the opener of a doubleheader Saturday. The team hadn't announced a Game 2 starter.
Reds: RHP Trevor Bauer (3-1) will make his 200th career major league appearance when he starts the first game of the doubleheader. The team hadn't announced a Game 2 starter.
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