Clayton Kershaw, the three-time Cy Young Award-winner whose post-season performance has never quite lived up to his Hall of Fame resume, has put the Los Angeles Dodgers on the brink of World Series victory.

The 31-year-old left-hander came through for a gritty Game 5 win over the Tampa Bay Rays on Sunday that gave the Dodgers a 3-2 lead and a chance to win Major League Baseball's best-of-seven championship series on Tuesday.

"He just grinded," manager Dave Roberts said of Kershaw's 5 2/3 innings on Sunday. "He just willed himself to that point."

Kershaw himself acknowledged his slider wasn't working well.

"Curveball, too, actually," he added. But he was able to do enough to help the Dodgers secure the victory and gain a chance to wipe away the memories of World Series defeats in 2017 and 2018.

"Any time you have any success in the post-season, it just means so much," Kershaw said. "That's what you work for, that's what you play for this month. I know what the other end of that feels like, too."

The generational pitching talent has had to listen to the whispers about his post-season performance get louder as the Dodgers failed to nab the game's biggest prize.

He has pitched plenty of outstanding playoff games, including a Game 1 gem against the Rays in which he gave up just two hits with eight strikeouts and one walk in six innings.

The Game 5 win gave him a winning post-season record of 13-12, and his six strikeouts took his career tally in the playoffs to 207 -- breaking the previous record of 205 held by Justin Verlander.

With a first World Series title beckoning, it was no wonder Kershaw said Monday's off day would be difficult."

"It's going be good for us, resetting our bullpen, which is good," he said.

"But sitting around, one win away from a World Series, is going to be hard, especially when you've been in the same hotel for four weeks now."

If the Dodgers do get over the line, it won't be in front of 50,000 ecstatic fans at Dodger Stadium, but in the neutral venue of Globe Life Field in Arlington, Texas, where the teams are in a controlled environment as the pandemic-disrupted season comes to a close.

But 11,500 fans are being allowed at the 40,000-capacity ballpark just south of Dallas -- Kershaw's hometown.

"I don't want to say it's working out the way that I wanted it to, just because being at Dodger Stadium would be awesome, too," Kershaw said. "But to get to have family and friends here, to get to have as packed a house as it can be and make it basically seem like it's all Dodger fans, is very special as well."