Kershaw, 31, now has sole possession of fifth place on the Dodgers' wins list, behind Brickyard Kennedy, Dazzy Vance, Don Drysdale, and Don Sutton.
* Hall of Famer
Tuesday's victory over the Toronto Blue Jays also marked the 22nd consecutive start to begin the season in which Kershaw has thrown at least six innings, the longest such streak by a National League southpaw since the strike-shortened 1994 campaign.
Kershaw, a three-time Cy Young Award winner and a former MVP - like Koufax - is in the midst of another remarkable season. The eight-time All-Star possesses a 2.71 ERA and a 3.47 FIP through 143 innings and entered Tuesday's game ranked ninth among qualified starters in WAR, according to FanGraphs.
The longtime ace now owns a 166-71 career record over 339 games (337 starts). Koufax retired after the 1966 season with a 165-87 record in 397 contests (314 starts) over his 12-year MLB career, which began in Brooklyn.