Schwarber's two-run shot in the eighth made it 4-0 and led to chants of "Kyle Schwarber! Kyle Schwarber!" from a vocal rooftop crowd in foul territory in left.
"He's a strong man and we've got a real powerful lineup," manager David Ross said, "and that's what happens when you start from pitch one and grind at-bats and try to see pitches and are on the attack as far as your approach."
The Pirates got three in the ninth on Colin Moran's two-run homer off Kyle Ryan and Gregory Polanco's run-scoring groundout. But Rowan Wick coaxed pinch hitter Jose Osuna into a fielder's choice for his third career save.
"This group doesn't quit," Pirates manager Derek Shelton said. "We continue to have good (at-bats) and have a chance to win the game late."
"It's going to be daily with him, daily conversations," Ross said. "He threw a pretty intense bullpen today trying to work out some things."
Chatwood had control issues in his first season with Chicago in 2018, but the right-hander was better last year. He is off to a great start in 2020, allowing one run and six hits in 12 2/3 innings over his first two outings.
"Obviously you want to get off to a good start, but I felt good second half of last year," Chatwood said. "I felt good in spring training and what I was able to continue doing during that off period, I felt like I kept getting better. And now obviously it's fun to put it in play against an opposing team."
The Pirates finished with six hits in their fourth loss in five games. They began the day with a major league-low .177 team batting average.
Moran said he remains confident in the Pirates' lineup.
"We have very talented hitters," he said. "I know it's the beginning of the season, so everything feels like it's more amplified."
Pittsburgh also lost Mitch Keller (1-1) in the third inning because of left side discomfort. The right-hander, one of the team's top young arms, was visited by a trainer after he bounced a curveball to Willson Contreras with two out. After a short conversation, he walked off the mound and was replaced by Chris Stratton.
The 24-year-old Keller surrendered long drives by Happ and Baez earlier in the inning. Happ's one-out shot traveled an estimated 405 feet, and Baez's 448-foot blast hit the batter's eye in center with two out.
"We're playing really good as a team," Baez said.
Pirates right-hander Michael Feliz also departed with an apparent injury after he was unable to record an out in the eighth.
Shelton said Keller and Feliz were being evaluated, and the team probably would have an update on Sunday.
Ross said Bryant would get a rapid response coronavirus test Sunday morning as a precaution, but the team thought it was just a stomach issue.
Cubs: LHP Jose Quintana (thumb surgery) threw 38 pitches in a bullpen session. He is scheduled for another bullpen on Monday. ... Contreras was hit on his left forearm by a pitch in the sixth, but he stayed in the game.
Steven Brault and Jon Lester start the series finale in a matchup of left-handers. Brault threw two scoreless innings for Pittsburgh on Monday night before its home opener was delayed by rain. Brault likely will be followed by right-hander Chad Kuhl, part of an early season experiment by first-year manager Derek Shelton. Lester (1-0) pitched five hitless innings in his first start Monday at Cincinnati.
Jay Cohen can be reached at https://twitter.com/jcohenap
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