Kershaw allowed just three singles in his eight innings, with only one runner allowed in scoring position, and that was thanks to a throwing error in the sixth inning. He threw just 101 pitches.
Kershaw extended his scoreless streak to 20 innings, and has allowed just one run in his last 29 innings.
He struck out exactly two batters in each of the first seven innings, then got three ground outs in the eighth. That snapped a string of eight straight innings with exactly two strikeouts and a streak of 18 straight innings with at least one strikeout.
Manager Don Mattingly chose to get closer Kenley Jansen an inning of work with a 4-0 lead in the ninth. Jansen allowed two hits, including a home run by Bryce Harper, his 27th home run of the season. Jansen did strike out three of his own to finish the game.
Harper was 0-for-3 with three strikeouts against Kershaw.
Kershaw has 34 strikeouts since his last walk, which came in the first inning on July 3.
Kershaw's only game with more strikeouts was during his no-hitter against the Rockies on June 18, 2015, when he strick out 15. The Dodgers franchise record for strikeouts in a game is 18, held by Sandy Koufax (twice) and , who last turned the trick on June 4, 1990.
Kershaw is the first Dodgers pitcher with at least 13 strikeouts in back-to-back games since Chan Ho Park from Sept. 24-29 2000.
The only Dodgers pitcher since 1914 with back-to-back starts of double-digit strikeouts and no walks was Vance on Sept. 11-16, 1930.
Kershaw has the fifth game in baseball this season with at least 14 strikeouts and no walks, joining Corey Kluber (18 strikeouts), Michael Pineda (16), Chris Archer (15) and Chris Sale.
The Dodgers backed Kershaw with three straight hits for a run in the second, then a three-run rally in the fifth, with Yasiel Puig delivering an RBI single in each frame.
Adrian Gonzalez didn't homer, but he did have three hits including a double. Justin Turner added three hits of his own, and Howie Kendrick had two singles and scored a run.
Yet another scoreless streak is on the line on Sunday, with Zack Greinke getting the start for the Dodgers in the series finale, in a fantastic pitching matchup against Max Scherzer of the Nationals.
Home runs: Bryce Harper (27)
WP - Clayton Kershaw (7-6): 8 IP, 3 hits, 14 strikeouts
LP - Doug Fister (3-5): 5 IP, 9 hits, 4 runs, 2 walks, 1 strikeout