Jaylen Brown goes up for a shot between Rui Hachimura, left, and Troy Brown Jr. during Boston’s 125-121 overtime win Saturday night at TD Garden. Michael Dwyer/Associated Press

BOSTON — Jaylen Brown scored 37 points, making a tying three-point play with 4.1 seconds left in regulation and adding 11 more in overtime as the NBA-leading Boston Celtics snapped a three-game losing streak by beating the archrival Los Angeles Lakers 125-121 on Saturday night.

Brown added nine rebounds, Jayson Tatum had 30 points and 11 rebounds, and Malcom Brogdon scored 15 of his 26 points in the second half of a see-saw game that had 19 lead changes – six in the fourth quarter – and 15 ties.

LeBron James had 41 points, nine rebounds and eight assists, and Anthony Davis had 16 points and 10 rebounds for the Lakers. Patrick Beverly scored 15 points, twice giving the Lakers the lead in the final minute of the fourth, but he also missed a foul shot that might have clinched it and was called for a technical foul to start overtime after the contentious last play of regulation, when the Lakers thought James was fouled on a drive to the basket.

Tatum made the free throw, and Boston never trailed in the extra period.

With Celtics Hall of Famer Paul Pierce cheering his former team on from the sideline and the team’s broadcasters – Boston’s Cedric Maxwell and L.A.’s Mychal Thompson – talking trash on press row, the Celtics swept their longtime rivals in the two-game season series.

Beverly hit a 3-pointer to give the Lakers the lead with 52 seconds left and then, after Boston tied it, scored on a putback dunk that made it 104-102 with 19 seconds to play. After Brown missed a 3, Beverly made one of two free throws; Al Horford missed a 3, and Brown scored on the putback and picked up a delayed foul call.

One game after missing a pair of free throws in the final seconds of a one-point game, Brown hit this one to tie it 105-all with 4.1 seconds to play.

The Lakers had a chance to win it in regulation, and James drove to the basket. He missed the layup – and the referees missed Tatum swiping his arm on the shot. An enraged James gesticulated wildly, and Beverly picked up a technical foul in the ensuing hubbub.

The Celtics (36-15) have the NBA’s best record despite losing their previous three games, including an overtime loss to the Knicks on Thursday night.

There was a vocal contingent of Lakers fans making noise when the visitors opened an 11-point lead in the third quarter. But they were outshouted by the locals when Tatum, who scored 15 in the third, including three 3-pointers, helped erase an 11-point deficit.

TIP-INS

Pierce was wearing what appeared to be shamrock pajama pants. … Westbrook missed his first six shots, as the crowd taunted him to shoot, before finishing with 12 points on 4 of 14 shooting. … Brown picked up his fifth foul on the first possession of the fourth quarter. … The Celtics beat the Lakers 122-118 in L.A. on Dec. 13. … The Celtics were without point guard Marcus Smart and big man Robert Williams III, who both have sprained ankles.