One of the NBA’s worst teams nearly knocked off the Celtics on their home floor Sunday.

Boston trailed the lowly New Orleans Pelicans late in the fourth quarter and needed a last-second stop to escape with a 120-119 victory at TD Garden.

The game, which pitted the defending NBA champions against the last-place team in the Western Conference, featured 21 lead changes and 14 ties. A five-second violation on Derrick White gave the 8-32 Pelicans a chance to win at the death, but CJ McCollum missed a contested layup as time expired.

White’s two late free throws proved to be the difference for Boston, which improved to 28-11.

Jayson Tatum scored a game-high 38 points on 14-for-30 shooting, including clutch makes on consecutive possessions late in the fourth, and added 11 rebounds. Kristaps Porzingis added 19 points, 11 rebounds and three blocks. Jaylen Brown had 16 points, eight rebounds and seven assists.

Brown’s even plus-minus was the highest of any Celtics starter. Boston did not outscore New Orleans with any of its top five players on the floor.

Al Horford and Payton Pritchard each scored 11 points off the Celtics’ bench. Pritchard finished as a plus-12; reserve center Luke Kornet was a game-best plus-13.

Trey Murphy III poured in 30 points to lead New Orleans, with Dejounte Murray adding 26, nine rebounds and eight assists. Zion Williamson had 16 points and five steals in his return from a team-imposed one-game suspension.

Murphy and Murray combined for 11 made threes, nearly equaling Boston’s team total. The Celtics went 13-for-44 (29.5%), shooting below 30% from 3-point range for the third time in four games.

The Celtics shot the ball dreadfully from deep in the first quarter, missing their first five triples and 10 of their first 12. Both of those makes were by Porzingis. It took nearly 11 minutes for any other Boston player to hit a shot from beyond the arc.

While the Celtics were scuffling, the Pelicans were uncharacteristically lethal from three. Ranked 26th in the NBA in 3-point shooting percentage and 27th in made threes per game, New Orleans went 7-for-12 in the first quarter, including a scintillating 5-for-5 start from Murray. Murray hadn’t hit more than three threes in any full game since last season.

Boston offset some of its perimeter woes with quality offensive rebounding, grabbing six in the first quarter to score seven second-chance points. Tatum found success on drives, scoring two tough layups and drawing a pair of fouls during a 13-point first. New Orleans led by as many as 11 points early, but the Celtics cut it to by the end of the first, then took their first lead five minutes into the second on a bank shot by White.

Brown helped key a 16-8 Celtics run by assisting on three short buckets by Kornet and converting a tough and-1 layup. But his turnovers on back-to-back possessions allowed the Pelicans to jump back ahead. Boston took a slim 62-61 lead into halftime, with 30 of their points coming from Tatum (17) and Porzingis (13).

Neither team led by more than four points for the first 11 minutes of the second half. Jrue Holiday was Boston’s main facilitator in the third quarter, feeding Tatum and Brown for fast-break dunks (the only points the Celtics scored in transition in the first three quarters) and later lofting a lob to Porzingis for a throw-down slam.

The Porzingis alley-oop, which came after a Murphy 3-pointer, kicked off a stretch in which Boston scored on five consecutive possessions, capped by a corner three from Horford that made it 85-82 C’s. Consecutive makes by Sam Hauser (corner three) and Tatum (baseline jumper) put the Celtics up five, but a buzzer-beating Javonte Green dunk off a Tatum turnover cut their lead to 90-88 heading into the final quarter.

Stops were hard to come by for Boston to start the fourth, with New Orleans getting points on its first five trips down the floor. Porzingis had a soaring dunk blocked by McCollum, leading to a Jose Alvarado three at the other end that put the Pelicans ahead 100-98.

Brown pushed the Celtics back in front with two free throws and a contested 6-footer, and Holiday followed with an up-close jumper in traffic to make it a five-point game. Two minutes later, Murray hit his first 3-pointer since the first quarter to tie the score at 110-110.

The Celtics rebuilt a four-point lead after White — who made just one field goal in the game — drew a foul and made both shots and Tatum sank a fadeaway jumper. But again, they couldn’t hold it. The typically reliable White committed an unforced turnover when he fumbled an inbounds pass into the front row of seats, and Tatum fouled Murray on an errant corner three. Murray hit all three free throws to put the Pelicans back ahead 115-113.

Tatum responded with back-to-back dunks bookending a Williamson turnover and a Murray miss. White hit what proved to be the game-winning free throws after pulling down a rebound after an off-the-mark Murphy three.

But the Celtics had to withstand one final scare. A Murray putback and two McCollum free throws cut their lead to one, and White was whistled for not inbounding the ball quickly enough, giving New Orleans one last shot. McCollum got to the rim but couldn’t finish, and the Celtics avoided what would have been their most humbling loss to the season.