Clayton Kershaw wins 15th as Dodgers top Brewers, 5-1

Dodgers Manager Don Mattingly isn’t ready to concede the season until the Dodgers are formally eliminated from playoff contention.

But with the Dodgers now 11 games under .500 with 39 games remaining, “we have to be realistic as an organization” that they’re unlikely to reach postseason play, Mattingly said.

Either way, the first-year manager said he expects no let-up in the Dodgers’ will to win. “For me, that cannot ever be compromised,” he said.

Dodgers ace Clayton Kershaw certainly didn’t let up Thursday as the left-hander tossed eight scoreless innings to lead the Dodgers past the Milwaukee Brewers, 5-1, and help them avoid being swept in their four-game series.

The 42,873 at sold-out Miller Park saw Kershaw scatter five hits, walk none and record six strikeouts to lift his league-leading strikeout total to 199.

The 23-year-old Kershaw also recorded his 15th win, tying him for the league lead with Roy Halladay of the Philadelphia Phillies and Ian Kennedy of the Arizona Diamondbacks.

Kershaw said it obviously helped that the Dodgers, typically starved for runs, gave him a lead. The team had scored only two runs in the prior three games.

“Five runs is huge for us and hopefully we’ll continue the momentum” as the team opens a three-game series Friday against the Rockies in Denver, Kershaw said.

Dodgers catcher Rod Barajas scored the team’s first two runs, starting with a solo home run in the second inning against Brewers starter Marco Estrada.

In the seventh inning, Barajas doubled against reliever Kameron Loe and scored on Jamey Carroll’s single. Kershaw then had a bunt single that Loe fielded, but the Brewers pitcher threw wildly to first base, allowing Carroll to score.

The Dodgers padded their lead with a two-run eighth inning against reliever Tim Dillard with singles by Andre Ethier, Matt Kemp and Aaron Miles and a sacrifice fly by Juan Rivera.

Milwaukee scored its run in the ninth inning against Dodgers reliever Javy Guerra when Ryan Braun tripled and scored on Prince Fielder’s sacrifice fly.

The Dodgers’ recent struggles included being swept at home by the Phillies this month, then losing three of four to the Brewers. The Dodgers entered Thursday’s play 131/2 games behind Arizona in the National League West.

“Obviously, we’re not going to concede the season in the sense of knowing that we’re not mathematically out of it,” Mattingly said.

“But I think we have to be realistic” and not expect that “all of a sudden now we’re going to go out and score six runs a game and sustain that through the last 40 [games] and win 36 out of 40 or something,” he said.

“I know it’s possible, and you know I’m the most optimistic guy as far as what I believe can happen,” Mattingly continued.

“But the situation we’re in, we’re going to be playing a young kid at short[stop],” either Dee Gordon or Justin Sellers, “and we’re going to get some kids up in September that we’re going to need to take a look at and try and make decisions into next year,” Mattingly said.

james.peltz@latimes.com