The right-handed Scherzer (4-1) allowed one run and four hits and walked three as the Nationals improved to 3-1 on a nine-game road trip.
Kershaw (1-3) gave up four runs and nine hits over seven innings. The left-hander struck out four and walked none.
Michael A. Taylor, Trea Turner and Ryan Zimmerman each had two hits and one RBI for Washington. Bryce Harper added a run-scoring single for his 19th RBI of the campaign.
Chris Taylor reached base four times on two singles and two walks for the Dodgers, who had a four-game winning streak halted.
Four pitchers followed Scherzer with right-hander Brandon Kintzler working a perfect eighth and left-hander Sean Doolittle tossing a flawless ninth for his fourth save.
Washington jumped on Kershaw for two runs in the first inning.
Turner smacked a double to left on the first pitch of the game, moved to third on a flyout and scored on Harper's single to right. Harper moved to second on a wild pitch and scored on Zimmerman's double to left-center field.
The Nationals added a run in the fifth when Taylor led off with a double, moved to third on Scherzer's one-out single and scored on Turner's surprise bunt single that left no Dodger covering first base.
Washington made it 4-0 in the sixth as Zimmerman and Matt Wieters reached with singles. Taylor delivered the key two-out RBI single with a liner over Kershaw's head that sailed into center field.
The Dodgers broke through in the bottom of the sixth despite Scherzer striking out the first two batters. Joc Pederson walked and Chase Utley singled before Yasiel Puig lined a single to left to score Pederson.
Los Angeles moved within 4-2 on Yasmani Grandal's run-scoring single in the seventh.
Washington's Wilmer Difo drew a bases-loaded walk with two out in the eighth off right-hander Pedro Baez to boost the margin to three.
Nationals third baseman Anthony Rendon (left big toe) missed his sixth straight game.
--Field Level Media
Washington | LA Dodgers | |
Max Scherzer | Player | Clayton Kershaw |
Win | W/L | Loss |
6.0 | IP | 7.0 |
9 | Strikeouts | 4 |
4 | Hits | 9 |
1.50 | ERA | 5.14 |
Washington | LA Dodgers | |
Michael A. Taylor | Player | Chris Taylor |
2 | Hits | 2 |
1 | RBI | 0 |
0 | HR | 0 |
3 | TB | 5 |
.500 | Avg | .667 |
Team | Hits | HR | TB | Avg | LOB | K | RBI | BB | SB | Errors |
Washington | 10 | 0 | 13 | .278 | 16 | 6 | 5 | 3 | 0 | 0 |
LA Dodgers | 6 | 0 | 9 | .188 | 20 | 12 | 2 | 4 | 0 | 0 |