Kershaw struck out a career-high 15 batters in the effort and walked none. The only batter to get to first base all night was Corey Dickerson, who reached on a throwing error by Hanley Ramirez to open the seventh inning.
"That was a really though play. Under normal circumstances, that was pretty close to a hit," Kershaw said after the game. Hanley did all he can. There is nothing you can really do about that."
After the error, Kershaw retired the final nine batters of the game, including five by strikeout.
"Clayton was just so dominant as the game went on, he had such a great breaking ball," said catcher A.J. Ellis. "The combination of his slider and curveball was the best I've seen. When you have those things going, nights like this are possible."
More on the no-hitter
There have been two no-hitters in baseball in 2014, and both have been thrown by Dodgers. In addition to Kershaw's masterpiece, teammate Josh Beckett no-hit the Phillies on May 25 in Philadelphia. It is the first time the Dodgers have had multiple no-hitters in the same season since 1956, when Carl Erskine and Sal Maglie turned the trick for Brooklyn.
The last team to have two pitchers throw complete game no-hitters in the same season was the 1972 Cubs, with Burt Hooton and Milt Pappas.
Kershaw won his fourth straight game on Wednesday and during the month of June is 4-0 with a 1.24 ERA to go along with 39 strikeouts and just one walk, in 29 innings.
"You like seeing good things happen to good people," Mattingly said. "He's special."