With one more victory or a Knicks loss, the Celtics (54-25) will clinch the No. 2 seed in the Eastern Conference playoffs. The Celtics will have a chance to make both of those things happen when they visit Madison Square Garden on Thursday night, Jayson Tatum’s first game in the building since rupturing his Achilles tendon there last May.

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For the Hornets, the final days of the regular season are more urgent. This loss dropped them to ninth in the conference, a half-game behind the Magic. But they could still vault as high as sixth place and escape the play-in tournament involving the seventh-through-10th-place teams.

With former Celtic Grant Williams defending, Jordan Walsh threw down a two-handed slam dunk for the Celtics during a third-quarter spurt in Tuesday night’s 113-102 victory over the Hornets at TD Garden.Danielle Parhizkaran/Globe Staff

And for much of the game against the Celtics their desperation seemed apparent.

“They came out and were trying to blow up screens,” Jaylen Brown said. “They came out playing with a different intensity level than we did to start the game. As we picked it up to match their energy, I think that’s what helped us pull away.”

Brown had 35 points and nine rebounds to lead the Celtics. The All-Star forward played the entire second half and 43:15 overall. It is common for teams to mix in some heavy workload games for their stars late in the regular season to prepare them for what is coming in the playoffs.

But after this game, coach Joe Mazzulla said he simply kept Brown in the game because he was playing well. Brown said he had not expected to play that much, but added that he has prepared himself for these situations.

“I’ve been taking care of my body all year,” he said, “and making sure that I’m available for my team.”

Tatum added 23 points for the Celtics, who made 17 of 42 3-pointers as a team and held the Hornets to just 15 points in the fourth quarter after surrendering 61 in the first half.

Backup center Nikola Vucevic played his second game since missing a month because of a broken finger and appears to still be knocking off some rust.

He missed a runner and a 3-pointer during his 0 for 6 first half and finished 1 for 10, with 2 points and seven rebounds in 22 minutes.

It will be important for Vucevic to eventually find his groove, and it makes sense the Celtics will try to prioritize that over the final few games of the regular season. But Luka Garza thrived off the bench in recent weeks with his screening and 3-point shooting, and if Vucevic’s struggles continue Mazzulla could eventually face a tough decision.

Against the Hornets, Vucevic played for 10:24 in the fourth quarter and Mazzulla was encouraged by his production, even if his shots were not falling.

“He’s got to get his legs underneath him,” Mazzulla said. “But I thought that fourth-quarter run there, his pick-and-roll defense was good. He got a deflection steal. He just felt more comfortable out there in playmaking, which comes with time.”

Hornets guard LaMelo Ball had 23 first-half points to give his team a 61-55 halftime lead over the Celtics in Tuesday night’s game at TD Garden.Danielle Parhizkaran/Globe Staff

LaMelo Ball poured in 36 points for the Hornets, but he was held scoreless in the fourth, with pesky defender Jordan Walsh deployed to slow him.

“He just understands that when he’s at his best defensively, he’s impacting the other team’s best player, he’s creating turnovers, he’s making things difficult for us,” Mazzulla said. “I thought he did a good job of that.”

The Hornets led, 87-80, with two minutes left when the Celtics crafted their most powerful run of the game. Payton Pritchard (12 points) hit back-to-back 3-pointers before Brown set up a two-for-one chance with a jumper with 33 seconds left. After a Kon Knueppel miss, Brown raced upcourt and cashed in the second chance with a buzzer-beating layup that capped the 10-0 burst.

The Celtics led, 96-94, early in the fourth before fully seizing control. A Tatum layup and 3-pointer sparked a 10-0 run that gave the Celtics a 106-94 edge, their largest. The Hornets never bounced back. In the fourth quarter they were 1 for 7 from the 3-point line, did not attempt a free throw, and committed four turnovers.

“I thought our defense kept us in the entire game, but I thought we took it to a different level,” Mazzulla said. “And then I thought connecting a better offense there made us even better throughout the second half.”

Adam Himmelsbach can be reached at adam.himmelsbach@globe.com. Follow him @adamhimmelsbach.