Justin Verlander is now the only player with more playoff strikeouts, recording 205 over his 187 2/3 innings.
The 32-year-old wound up recording eight strikeouts over six innings, allowing one run on two hits and one walk. That lifts Kershaw to 201 in his career during the postseason.
Kershaw entered Tuesday's start with a 4.31 career ERA in the postseason. The three-time Cy Young winner has adjusted the narrative in 2020 with some dominant performances, authoring a 3.32 ERA through his first three starts, striking out 23 over 19 innings.
The eight-time All-Star improved to 2-2 over six World Series starts.