SAN FRANCISCO -- It took a statistical achievement that LeBron James had never reached before in 1,463 career regular-season games, an extra 10 minutes of game time and two swished free throws with 1.2 seconds remaining before the Los Angeles Lakers star could claim victory over his longtime nemesis, Stephen Curry and the Golden State Warriors.

The Lakers won 145-144 in double overtime on Saturday with James putting up 36 points, a career-best 20 rebounds and 12 assists, edging Curry's game-high 46 points -- including 15 in the OT periods -- in an instant classic between the two surefire Hall of Famers.

"It's something I'll be able to talk about with my grandkids," James said of his matchup with Curry. "When you talk about me being able to compete versus one of the greatest players to ever play the game."

The game was scheduled as part of the NBA's Rivals Week, and it did not disappoint, with the 39-year-old James and the 35-year-old Curry looking every bit as masterful as they did when their teams met in the NBA Finals four consecutive times.

"It's been a treat to go against one of the greatest to ever play this game," James said. "For us to continue to push each other at the state of our careers, you don't take it for granted because you don't know how many times you're actually going to get the moment to actually be on the same floor with such a talent."

While James' Lakers won the championship in 2020 for his fourth ring and Curry's Warriors won it all two years later for his fourth title, both players' teams have fallen on challenging times.

The Lakers' win lifted them to 24-23, ninth in the Western Conference. The loss dropped the Warriors to 19-24, No. 12 in the West.

For a night, however, the team records didn't reflect the competition on the court.

"Every year that we get to do this and go back and forth, the battles -- the Finals runs, the playoff battles last year -- after the horn sounded tonight there was a little laugh of, I can't imagine a scenario where a game like tonight happens, [with] him in Season 21 and me in Year 15," Curry said. "You look forward to the battles, but you also appreciate the mutual respect of what it takes to keep doing what you're doing at this level. Only a few people know how hard it is. I'm happy to be in that group."

James' clutch free throws were needed because of Curry's brilliance down the stretch. He scored a layup over Anthony Davis with 5.9 seconds remaining in regulation to force overtime, and in overtime he hit a 3 with 53.4 seconds left to cut L.A.'s lead from four to one, setting up Klay Thompson to tie the score a couple of possessions later to extend the action. In the second overtime, Curry hit a 3 from the top of the key -- his ninth of the night -- to put the Warriors up by one with 5.9 seconds to go.

That's when James, who missed a potential winning fadeaway shot from midrange at the end of the first overtime, drove on Draymond Green and got fouled to set up the final free throws.

"I was able to get a little bit of an angle on the second OT and I was able to drive, taking a Eurostep kind of back to the right hand, and I was able to get a foul called on Draymond and stepped up and made the free throws," James said.

The win jump-started a crucial six-game road trip for L.A. as it tries to make up for its monthlong tailspin that followed its in-season tournament championship victory in Las Vegas.

The Lakers will visit the Houston Rockets on Monday and hope that Davis, who had to leave the game after experiencing hip spasms, can play.

But the night provided a chance to look back, rather than look ahead, as James and Curry added another chapter to their interwoven story.

"Credit to LeBron for what he's doing at his age. I mean, that guy is a freak of nature in terms of his ability to play at this level for so long. Same with Steph," Thompson said. "When you're younger, you don't ever really think that basketball will stop because it's what you love. It's all you do. But when you get to your 30s, you realize there's an end point to being an athlete. Knowing that, I am very grateful to step on the floor with those guys and play against LeBron."