Mike Moustakas hit a three-run homer in the first inning as Darvish's seven-start winning streak was snapped.
Bauer (4-3) struck out 10 and walked none in 7 2/3 innings while tying his season high with 112 pitches. The right-hander dropped his three previous starts, including a 3-0 loss to Darvish on Aug. 29 in Cincinnati.
"That was fun to watch," Cincinnati manager David Bell said. "We needed a win and he did it against a good team.
"In a game like this, when you have two of the best (pitchers) in baseball, there was something a little bit different about Trevor. He rose to the occasion."
Bauer allowed just one hit -- a leadoff single in the fifth by Victor Caratini -- through seven innings. In the eighth, Bauer gave up a one-out single to Jason Heyward and was pulled after Ildemaro Vargas singled with two outs to put runners on the corners.
Raisel Iglesias worked the ninth for his sixth save.
"He really established his heater," Cubs first baseman Anthony Rizzo said of Bauer. "He was locating it really well first time around and he started mixing in everything else the second, third time around. He's a really good pitcher and he was on tonight."
Darvish (7-2) allowed three runs and two hits in six innings, walking three and striking out nine. All three runs and both hits came in the first inning. After that, the right-hander retired 16 of the final 17 batters he faced. The only blemish was a two-out walk to Brian Goodwin in the fourth.
Darvish allowed only five runs in 46 innings (an 0.98 ERA) during the winning streak. He entered leading the NL with a 1.44 ERA.
"I couldn't control my body in the first inning," Darvish said. "I tried to figure it out, but I couldn't."
Darvish had walked a total of eight batters during the previous seven starts -- compared with 58 strikeouts -- but issued back-to-back, one-out walks in the first. One out later, Moustakas took advantage of a hanging breaking ball for a three-run drive.
"As soon as Moose hit that ball, I said, `All right, I can make this stand up," Bauer said. "That was the goal. That helped lock me in."
Heyward returned to the Cubs' lineup after experiencing shortness of breath and light-headedness in Sunday's game against St. Louis. The veteran outfielder passed a series of tests over the last few days -- including multiple COVID-19 tests -- and was cleared to rejoin the team.
Heyward was concerned about possibly having the coronavirus after experiencing shortness of breath during his first at-bat Sunday. "It came out of nowhere," he said. "Yes, naturally, that was a big concern of mine, for sure."
CLEMENTE DAY HONORS
Heyward and the Reds' Tucker Barnhart were named their team's nominees for the Roberto Clemente Award, which is given annually to the player who best represents the game in character, community involvement and philanthropy.
Jose De Leon and Michael Lorenzen of the Reds and Javier Baez and Victor Caratini of the Cubs wore No. 21 to celebrate Clemente Day. All players of Puerto Rican heritage are allowed to wear the number to celebrate the late Hall of Famer. "Hopefully next year, we get to see everyone wear it," Heyward said.
Reds: LHP Wade Miley (shoulder sprain) threw a side session. "I got a good report," Bell said. "His next step may be to rejoin us. He's passed all the tests." ... LHP Jesse Biddle (shoulder) also continues to improve, but there's no timetable for his return.
Cubs: 3B Kris Bryant was held out of the lineup after being hit with a pitch on the left elbow by Tyler Mahle in the third inning Tuesday night. Manager David Ross said he decided to sit the struggling slugger as a precaution. "Some guys like to push through," Ross said. "He was pretty sore last night, so I wanted to take that off his plate."
Cincinnati veteran Sonny Gray (5-2, 3.19 ERA) takes on Cubs rookie Adbert Alzolay (0-1, 2.08) in the finale of the three-game series Thursday night.
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