ARLINGTON, Texas -- Say what you will about Clayton Kershaw's performance in October, but he now holds the record for postseason strikeouts.

The Los Angeles Dodgers' ace moved past Justin Verlander for the all-time lead while giving up only two runs in 5⅔ innings against the Tampa Bay Rays in Game 5 of the World Series on Sunday night. Kershaw struck out six batters, giving him 207 career postseason strikeouts in 189 innings. Verlander has 205 strikeouts in 187⅔ career postseason innings.

"It just means I've been on great teams that have gotten to go to the postseason a lot and I've gotten a lot of starts in the postseason," Kershaw said after helping the Dodgers to a 4-2 win and a 3-2 World Series lead. "It's just a special thing to be part of a team like this and be part of some of those names."

The Rays were threatening against Kershaw in the fourth inning, putting two on with none out while trailing by only a run, but Kershaw induced a shallow pop-up and recorded a strikeout, then threw out Manuel Margot as he attempted to steal home. The 32-year-old left-hander then retired the next five batters in order.

Dodgers manager Dave Roberts was booed by a very pro-Dodgers crowd at Globe Life Field while removing Kershaw in favor of Dustin May with two outs in the sixth, though at least part of their hostility was undoubtedly rooted in Roberts' pitching decisions from Game 4. May, Victor Gonzalez and Blake Treinen went on to retire 10 of the 13 batters they faced to seal the victory.

Kershaw entered with a 5.40 ERA in his World Series career but has gone 2-0 with a 2.31 ERA against the Rays, winning two games in the same postseason series for the first time in his career.

"The off-day is going to be hard for us tomorrow," Kershaw said. "It's going to be good, obviously, for resetting our bullpen and things like that, which is huge. But sitting around one win away from a World Series is going to be hard, especially when you've been at the same hotel for four weeks now."