Last Saturday, the Celtics barely scraped past one of the worst teams in the NBA, needing overtime to put away the two-win Toronto Raptors.

They had similar trouble Friday against another Eastern Conference cellar-dweller.

Boston endured one of its worst shooting performances of the season — including a garish 0-for-10 showing from 3-point range by Jayson Tatum — and trailed the Washington Wizards for much of the night before pulling away to win 108-96 at Capital One Arena.

“It’s good to win a game when you’re playing at your best offensively, and we had three 25-point quarters defensively,” Celtics head coach Joe Mazzulla told reporters after the game. “You’ve got to win different ways, and winning down the stretch and doing that with your defense is good.”

The rock-fight victory kept the Celtics in contention in the 2024 NBA Cup, and a string of late free throws helped them pad their point differential — a key tiebreaker to determine the eight quarterfinalists. They improved to 2-1 in NBA Cup group play with a plus-14 differential and one game remaining: next Friday at Chicago.

Jaylen Brown powered the Celtics with 31 points, 11 rebounds and five assists, capped by a clutch 19-footer with less than a minute remaining that all but ended Washington’s upset bid. Tatum struggled mightily as a perimeter shooter but was a team-best plus-20 in the win, finishing with 16 points, nine rebounds, eight assists and two steals.

Luke Kornet, a healthy DNP in Tuesday’s win over Cleveland, was an impact player in his 24 minutes off the bench, steadying the Celtics during a sluggish and mistake-filled first half.

As a team, Boston shot 42.4% from the floor and 23.9% from three and tied their lowest scoring output of the season against a Wizards team that came in ranked dead last in the NBA in defensive rating and net rating.

Washington built an early lead thanks to some scattershot Celtics shooting, as Boston generated quality looks but made just one of its first seven 3-pointers. Tatum started 1-for-5 and 0-for-3 from three, and the Celtics went nearly five full minutes without a made field goal, during which Washington outscored them 12-2.

Hauser ended that drought with a corner three, and that sparked a 12-2 run in Boston’s favor, with 10 of those points coming from Hauser and fellow bench scorer Payton Pritchard. The Celtics led 29-27 after one.

Momentum then shifted back toward the underdog hosts, thanks in part to ex-Celtic Malcolm Brogdon. The former NBA Sixth Man of the Year, who was part of Boston’s package for Jrue Holiday last summer, scored 13 first-half points against his former team, helping Washington build an 11-point lead midway through the second quarter.

Wizards big man Jonas Valanciunas also was a handful for fill-in Celtics center Neemias Queta, who got the start after Al Horford was a late scratch due to illness. Valanciunas and Brogdon — the oldest rotation players on a rookie-laden Wizards squad — combined to grab four offensive rebounds against Queta on a single possession that ended in a Brogdon layup.

Kornet subbed in for Queta shortly after that sequence and helped snap the Celtics out of the malaise that defined their first half. He corralled an offensive rebound and kicked it out to Brown for an open three that ignited a 13-0 Celtics run.

That spurt included a no-look alley-oop dunk and two defensive boards by Kornet. He also was defending Wizards guard Bub Carrington on the perimeter when Carrington was whistled for traveling, getting a chuckle out of the affable 7-footer. After a Corey Kispert layup stopped the bleeding for Washington, Kornet immediately slammed home another dunk off a nice feed from Brown.

Despite those quality minutes from Kornet, who was a plus-11 in the first half and got the nod over Queta to start the third quarter, the Celtics managed just 49 first-half points against the Wizards’ typically leaky defense. The Wizards held a 51-49 lead at half, and neither team led by more than three points until the final minutes of a tightly contested third quarter.

That third quarter featured the first meaningful minutes in nearly two weeks for Xavier Tillman, who’s largely been out of Mazzulla’s rotation since the end of October. Thirty-six seconds after checking in, Tillman blocked a Jordan Poole layup, springing Hauser for a 3-pointer at the other end. He added another block later in the game, though he also had some defensive lapses over his nine minutes.

Those were the first stats Tillman recorded in any category since Nov. 8. His most recent action before Friday came with the Celtics’ G League team, which he joined for one practice this week to aid Kristaps Porzingis in his rehab.

“He’s been working hard, and I felt like the game needed something different,” Mazzulla told reporters. “Those guys are always ready. We wanted to be a little more switching, and the last time we played them, we played him and Luke together, and he did some great things on the defensive end, especially in the Valanciunas minutes. So I just wanted to win those minutes in the fourth quarter, and it’s a credit to him, just working hard and being ready. I thought he gave us some good stuff.”

Also in the third quarter, Mazzulla was hit with a technical foul for reaming out referee Ed Malloy. The Celtics coach, who thought Brown had been fouled on a layup attempt, had to be held back by assistants Tony Dobbins and Sam Cassell. The Celtics proceeded to score 13 of the next 17 points and took a 75-72 lead into the fourth quarter.

“(The tech) changed the energy in the arena. Did you feel that?” Mazzulla told reporters. “… It wasn’t really about energizing the team; I think it was just manipulating the environment. I thought it was what the environment needed at the time.”

Boston finally was able to create some separation in the final eight minutes. Derrick White hit his first two threes of the game after an 0-for-7 start, three different Celtics notched steals, and Tatum and Brown both nailed tough, contested, midrange fadeaways as part of a 15-point fourth quarter for the duo. Brown’s over Kyle Kuzma was the dagger, putting the Celtics ahead 99-92 with 46.4 seconds remaining and triggering a parade of Wizards fouls.

Next up for Boston: a Western Conference back-to-back at TD Garden. Anthony Edwards and the Minnesota Timberwolves come to town on Sunday, followed by a matchup with the Los Angeles Clippers on Monday.