In the eighth inning, Kershaw struck out Drew Stubbs for the first out. Josh Rutledge then lined a ball down the left field line, the closest thing to a hit all night, but it went foul. Rutledge went on to strike out. Kyle Parker grounded to first to end the inning.
Kershaw has a season-high 14 strikeouts so far and has retired 24 of the 25 batters he has faced. The only batter to reach base was Corey Dickerson, who reached on a throwing error by shortstop Hanley Ramirez in the seventh inning.
The Dodgers ace left-hander, in addition to seeking his fourth straight win and a series sweep for the Dodgers, is vying for the second no-hitter by a Dodgers pitcher this season. Josh Beckett no-hit the Phillies on May 25.
In the ninth inning, Kershaw is due to face DJ LeMahieu, the pitcher's spot in the batting order and Dickerson.
The last time the Dodgers threw two no-hitters in the same season was back in Brooklyn in 1956, when Carl Erskine no-hit the Giants on May 12 and Sal "The Barber" Maglie no-hit the Phillies on Sept. 25.