LOS ANGELES -- Dodgers ace Clayton Kershaw looked at the final results from Los Angeles' win on Sunday and series sweep of the Chicago Cubs, and he viewed it the best way possible.

"It was a great series win," Kershaw said after the Dodgers' 9-4 victory. "No one gave up a run but me."

Indeed, the Dodgers shut out the Cubs in the first two games, and the bullpen worked 4 2/3 scoreless, hitless innings after Kershaw left the Sunday game.

For Kershaw as well as Cubs starter Jon Lester, the series finale was something from a different reality. A pitching duel seemed on tap, but neither got past the fifth inning. The teams combined for seven home runs that accounted for all 13 runs, Lester giving up two and Kershaw three.

Kershaw had one of his worst outings in his career, allowing 11 hits and four runs in 4 1/3 innings. He left the game with a two-run lead and two Cubs in scoring position. Lester allowed seven hits, two walks and six runs on a pair of three-run home runs, throwing just 76 pitches in 3 1/3 innings.

The Dodgers won because their home runs produced more and the bullpen was stellar behind Kershaw, most notably Josh Fields, who inherited that two-on, one-out situation in the fifth and struck out Javier Baez and Kris Bryant to end it.

"They did a great job," Kershaw said of the bullpen. "Games like this are a part of baseball, sometimes they don't go the way you expect. Josh came into a high-stress situation and got the big outs, and everyone down the line did their job."

Dodgers manager Dave Roberts said of Kershaw, "Initially his velocity was good. But his first pitches were broken-bat hits, and it created a stressful situation which never should have manifested itself.

"They hit a few balls hard after that and grinded back. It was billed as a pitchers' duel, but these are good hitting teams and they squared up all day."

Willson Contreras homered in the second for a 1-0 Cubs lead, but Los Angeles' Cody Bellinger hit a three-run shot, his 10th of the season, in the bottom of the second to make it 3-1, and Enrique Hernandez hit a three-run shot, his fourth, in the third to make it 6-1.

Baez hit his eighth home run in the fourth and Anthony Rizzo his 12th, a two-run shot, in the fourth to make it 6-4. Kershaw came back out for the fifth but allowed two singles. Fields (2-0) doused that rally, and Sergio Romo, Adam Liberatore and Kenley Jansen followed suit with hitless relief.

Dodgers catcher Austin Barnes hit a solo homer in the fifth to make it 7-4, and Yasiel Puig added a two-run shot in the seventh to make it a 9-4 game.

Puig wasn't in the starting lineup. Franklin Gutierrez got the start in left, but he exited after the top of the first due to an illness.

Puig entered, and he singled in addition to his home run. He also made a nice leaping catch in the right field corner on a rope by Rizzo in the sixth.

"I haven't been helping the team much on offense, so I do what I can on defense," Puig said.

The Cubs took the loss and the game in stride. Manager Joe Maddon praised the Dodgers' ability to find ways to win regardless of how the nine innings play out.

"That's a good club," Maddon said. "We knew that coming in, and they're playing very well right now."

Chicago third baseman Kris Bryant wasn't too down about the sweep, which followed the Cubs winning seven of nine.

"I don't see any reason to worry," Bryant said. "There are good years and bad years, and good weeks and bad weeks. We're off to an average start, but we're not terrible.

"We're probably a little spoiled by the start we had last year, but it's a long season. We know we're capable of playing well. We had a good homestand before coming here. It'll be OK."

NOTES: The win was the Dodgers' ninth in their last 11 games. They went 8-2 on their just-completed homestand. The Dodgers are 21-8 at home this year. ... Chicago was swept by the Dodgers in a series for the first time since 2012. ... The Dodgers rested several starters with Cubs LHP Jon Lester starting -- C Yasmani Grandal, 1B Adrian Gonzales and OF Yasiel Puig. ... Dodgers CF Chris Taylor, who had recently assumed the leadoff spot with his hot May, batted third in the order for the first time in his career. He went 1-for-5. ... Javier Baez was back in the Cubs' lineup at second base. Rookie Ian Happ started in left and hit cleanup. Happ was the only Cub who struggled against LHP Clayton Kershaw, striking out three times.