LOS ANGELES — Clayton Kershaw doesn’t feel like a potential no-hitter is serious until it lasts through six innings. Before that, it’s just the everyday dominance that Dodgers fans have come to expect over his 13 years in blue.

Although Kershaw’s latest no-hit bid ended one out shy of the serious innings, the veteran ace put together another historic performance that indicates he’s healthy, sharp — and perhaps just as good as ever.

Kershaw reached two career strikeout milestones and held the Diadmondbacks hitless into the sixth inning Thursday night, leading the Dodgers to a 5-1 win for their fifth straight victory.

While racking up eight strikeouts over six scoreless innings, Kershaw became the 39th pitcher in major league history with 2,500 strikeouts when he fanned Nick Ahmed in the second. The left-hander then caught and passed Christy Mathewson (2,502) for 38th place on baseball’s career list by getting Carson Kelly and Tim Locastro in the third.

Kershaw didn’t know exactly what to say about seeing his name next to Mathewson, the New York Giants Hall of Famer whose playing career ended 104 years ago.

“It’s cool, it really is,” he said. “It’s just hard for me think about or wrap my head around. Getting to see your name on different types of leader boards is cool. It’s just hard to grasp, really.”

The three-time NL Cy Young Award winner has thrown 15 consecutive scoreless innings since Aug. 20.