"I've been saying it all along," Maddon said. "I know we can play with the big boys in this league, but you've got to prove it. We have played less effectively against teams that have been struggling this year, and we've got to stop that."
The Cubs won three of four in this series. Bryant finished the series with six hits, a .282 average and feeling better at the plate.
"It just comes along when you're playing at this level. You feel more comfortable," Bryant said. "And I definitely feel more comfortable out there."
Jason Motte pitched a perfect ninth for his first save since 2012, when he led the NL with 42 for St. Louis before getting hurt. Closer Hector Rondon threw a perfect eighth — a day earlier, Maddon said he might put the right-hander in some lower-pressure situations to get settled.
"I just wasn't locating," Zimmermann said. "My breaking pitches were terrible. It's going to happen when you don't have all your pitches, and I just wasn't sharp today."
This was his first loss since April 18.
Coghlan came up against Zimmermann with the bases loaded and no outs in the fifth and hit a two-run single that put the Cubs up 4-2. Yunel Escobar helped the Nationals with an RBI single in the bottom half.
The Cubs made it 6-3 with two in sixth against Blake Treinen. He threw a bases-loaded wild pitch for one run, and Castro drove in another with a single to left. Left fielder Michael A. Taylor threw out Miguel Montero at the plate on the same play.
Washington center fielder Denard Span exited when his back locked up on him going up the dugout steps to start the eighth. That forced manager Matt Williams to move Taylor to center and put Danny Espinosa into left field for the first time in his career.
Williams shrugged off talk of being worried by his team's recent troubles. He said it's just part of a normal baseball season.
"I'm not concerned," he said. "What we need to do is play every day. It's been a little rough for us recently, but there's no reason we can't pull out of that, too. It's the way the game goes sometimes."
THE FIRST TIME
Williams has often praised Danny Espinosa's versatility, but he had to put him in left field for the first time ever. When Span left, Taylor moved from left to center and Espinosa entered. "Just (was trying) to get the job done, and not over-think it," he said. "Outfield's completely new for me."
Nationals: Escobar returned to the starting lineup after missing two games with a sore right wrist that he injured on a checked swing Thursday night. ... RHP Doug Fister (forearm tightness) threw a rehab assignment at Triple-A Syracuse Sunday, going 3 2-3 innings and giving up two runs on seven hits with six strikeouts. ... 1B Ryan Zimmerman was given a day out of the starting lineup. His foot injury (plantar fasciitis still bothering him, but he said it's nothing bad.
Cubs: LHP Jon Lester (4-4, 3.86) opens the series in Detroit on Tuesday while trying to bounce back from a shaky June 3 start when he gave up six runs on nine hits in five innings in a loss to the Marlins. That came after a strong month of May where he went 4-1 with a 1.76 ERA.
Nationals: RHP Max Scherzer (6-4, 1.85) starts the interleague series at Yankee Stadium, having won five of his last six starts. He's among major league leaders in several categories, including ERA (third) and strikeouts (fifth, 90).