Chicago eked out its lone run in the first inning on a night when the two squads combined to go hitless with runners in scoring position. An RBI groundout by Cody Bellinger with runners on second and third plated the decisive tally.
That was the only run allowed by Corbin Burnes, who successfully navigated traffic in his seven innings of work. Burnes allowed eight hits, walked two, and struck out seven.
Justin Steele also threw the ball well for the Cubs.
It seemed for a moment in the second inning Steele was at risk of leaving the game after a liner by Victor Caratini caught him in the leg, but the left-hander stuck around to punch out eight Brewers in six shutout innings.
The Brewers had a couple of near misses against Steele, including a deep fly ball by Tyrone Taylor in the fifth that Ian Happ caught against the left field wall.
Statcast pegged the ball as a home run in 28 out of 30 parks, but on a cool night with the wind blowing in, it stayed in the yard at Wrigley Field.
Joey Wiemer crushed a ball to deep left the following inning, this one with the distance to leave the yard, but he pulled it just foul.
From there, the offense could not muster much against the Chicago bullpen, recording just one baserunner against the trio of Mark Leiter Jr., Julian Merryweather, and Adbert Alzolay.
The Brewers look to return to winning ways in the rubber match on Wednesday afternoon. Brandon Woodruff starts opposite Kyle Hendricks. First pitch is scheduled for 1:20 p.m. CT.