LOS ANGELES -- Another dramatic chapter was written in the long, storied history of the Los Angeles Lakers and Boston Celtics' rivalry on Tuesday night.

The Celtics won 122-118 in overtime in a game Boston appeared to have no business losing -- then no business winning after a wild comeback by L.A.

Boston, led by Jayson Tatum's 44 points, outscored L.A. 12-8 in the extra period to pull out the victory.

"That game just says a lot about our experience and mental toughness," said Jaylen Brown, who added five of his 25 points in overtime. "That's a tough and perfect way to close out our road trip."

The Lakers trailed the Celtics by as many as 20 points in the third quarter but used an 18-0 run through the end of the third to the beginning of the fourth to take control, going ahead by as many as 13 with 4:25 remaining in regulation.

"We gave ourselves a chance to win," LeBron James said. "We didn't close it out. But loved our effort. I loved our tenacity in the second half and put ourselves in a position to win a ballgame playing against a great team."

L.A. seemingly had a chance to seal the win with Anthony Davis at the line with 28 seconds left and up by two points, but Davis -- who was 11-for-13 on free throws on the night at the time -- missed them both.

"I haven't thought about the rest of the game," a crestfallen Davis said after the loss. "Make two free throws, go up four, different ball game. To me, the rest doesn't matter. Had a chance to ice the game and missed both."

The misses set up a game-tying pull-up jumper by Tatum with 17.1 seconds remaining. L.A. then worked the clock down to get James a potential winner at the buzzer, but his 3-point attempt didn't go down.

Much like in the Lakers' loss at the Philadelphia 76ers last week, when L.A. surmounted a furious comeback to force overtime only to fall apart in the extra session, the Celtics broke the game open to close things out.

"Games aren't won or lost in the fourth quarter or overtime," Celtics coach Joe Mazzulla said. "We have to be elite at managing the end of the third, beginning of the fourth quarter. That is where NBA games are won and lost, and we didn't do a good job managing that part of the game. So we'll take the positives of how we worked to get back in the game and then managed a run to end it, but we'll also focus on that stretch."

Davis also missed a go-ahead free throw with 3.1 seconds left in regulation against Philadelphia, and he shouldered the blame for both losses.

"Boston is a great team. Philly's a great team. Two great teams in the East," Davis said. "Got a chance as a team, but me personally, to kind of seal both games. Missed one in Philly, missed both tonight. Both resulted in losses."

Russell Westbrook (20 points, 14 rebounds, 5 assists, 4 blocks) scored the first four points in overtime to give L.A. a 114-110 lead, but the Lakers couldn't sustain the momentum.

Davis finished with 37 points and 12 rebounds, and James had 33 points, 9 rebounds and 9 assists.

Lakers coach Darvin Ham played Davis all 29 minutes in the second half and overtime, and rested James for only 2 minutes, 28 seconds over that span.

Davis refused to use exhaustion as an excuse for his misses, but Ham said he should have worked in more rest for the group he was riding during the comeback.

"Strategically, trying to see how we can wisely use our timeouts and give them breaks that way," Ham said. "I could have done a better job in certain instances in using my timeouts quicker. But that falls on me. Got to get better in that regard."

The Celtics came into the night with an NBA-best 21-7 record but had dropped two games in a row, at the Golden State Warriors and at the LA Clippers.

"That's a prideful group over there," Ham said of Boston before the game. "I wholeheartedly believe that they're not pleased at all. Not just with the Clippers loss but with the loss before that against the Warriors. We know we're going to have our hands full."

It was the second time that the Lakers lost a game in which they led by double digits with five minutes to go in the fourth quarter this season. The rest of the NBA has done that twice combined this season, according to research from ESPN Stats & Information.

Despite the gut-punch nature of those outcomes, Westbrook said there is still reason for optimism within the locker room.

"If you're a competitor, you should believe," Westbrook said. "But I can't speak for everybody. I know for myself, as long as I'm, God willing, able to compete, then I'll do that 'til it's all said and done. But I'm pretty sure guys believe. It's just about creating some consistency across the board."

Information from The Associated Press was used in this report.