NEW YORK — With five seconds remaining in the first quarter of Saturday’s Game 3 at Madison Square Garden, Payton Pritchard received the ball deep in the backcourt and took off.

He looped toward the opposite sideline, sprinting past Knicks guard Miles McBride. Once he reached New York’s 3-point line, center Mitchell Robison rotated over to help and force Pritchard away from the paint. Pritchard decelerated, paused and, using Robinson’s momentum against him, lofted a high-arcing fallaway jumper over the outstretched arms of both defenders as the horn sounded.

Swish.

It was Pritchard’s 16th made jumper in the final second of a quarter over the last two seasons, the most of any Boston player. This one gave the Celtics a 16-point lead — and set the tone for the most productive postseason performance of the NBA Sixth Man of the Year’s career.

Pritchard went on to set playoff career highs in minutes (35), points (23), made field goals (8-for-16) and made 3-pointers (5-for-10) as the Celtics trucked the Knicks 115-93 for their first win of the Eastern Conference semifinals.

“Payton was huge,” teammate Jaylen Brown said postgame. “Payton was great. New York likes to be — they’re physical. They’ve got some big guards, wings that like to load up on the ball. The level of physicality is higher. So you’ve got to be able to make those passes and be able to make those shots and make those plays. Payton did a great job of that tonight.”

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Pritchard played the final 18:35 of the first half, then logged another unbroken shift that stretched from the 5:03 mark of the third quarter to the 3:13 mark of the fourth. He then returned to the court in garbage time, closing out the win alongside deep reserves Baylor Scheierman, Torrey Craig, Neemias Queta and Jordan Walsh.

Asked about Pritchard’s increased usage — he played 24 minutes in Game 1 and 22 in Game 2 — Celtics head coach Joe Mazzulla said starting guard Jrue Holiday’s foul trouble was a contributing factor. Holiday, who picked up his third foul a minute into the second half, played 25 minutes in Game 3, 10 fewer than any other Boston starter.

“Our sub patterns are always flexible,” Mazzulla said. “Tonight, Jrue had three fouls. Payton was good, you’re just — at times, you go with what makes the most sense. Just the flexibility of what we’re able to do. But he played really well on both ends of the floor for us. There was a little bit of foul trouble there, so we were able to go to some different stuff.”

Pritchard’s focus, he said, was to play aggressively and capitalize on open looks without being reckless with the ball. He did not commit a turnover across his 35 minutes.

“Just got to maintain my aggressiveness, any chance I get,” he said. “Attack the paint. I’ll always be hunting the three ball, obviously, but I thought I did a good job of sometimes getting in the paint, making a play. For me, it’s just about energy coming in. If I got to get a rebound, get an assist, get a stop, hit a big shot, got to be ready for everything.”

His mindset entering Game 4 on Monday night, when the Celtics will have a chance to tie to series at 2-2 before it shifts back to Boston for Game 5?

“You wouldn’t want to be in any other position as a competitor,” Pritchard said. “This is the best moment you can be in, down 2-0, backs against the wall. You just bring it, and I think we’re all prepared for it and we knew the task at hand, so we did a good job (in Game 3). Now, we’ve got to move on and do it again.”

Celtics more poised

One obvious improvement for the Celtics in Game 3 was their team-wide shooting. After going an ugly 25-for-100 from 3-point range over the first two games, they doubled their long-range field-goal percentage on Saturday, making 20 of their 40 3-point attempts.

They also cut down on the sloppy turnovers and defensive breakdowns that, along with their erratic shot-making, helped the Knicks overcome 20-point third-quarter deficits in Games 1 and 2.

New York staged several mini-rallies after halftime — most notably an 8-0 surge early in the third quarter and a 9-3 run to start the fourth, the latter of which featured three straight made threes — but Boston did not allow any to develop into a legitimate comeback. The Celtics led by 20-plus points for the entire second half.

“I think we had much better poise this game,” Al Horford said Sunday in a video conference. “Poise was key for us. I feel like we really executed when we needed to. Defensively, we were solid, and we were able to control those parts of the game.”

Mazzulla agreed.

“Game 3, they had seven points in transition as opposed to 28 in Game 2,” the coach said. “We didn’t have 11 live-ball turnovers, and we won the end of quarters 8-3. That makes a huge difference against a team like New York.”

Hauser upgraded

Sam Hauser is on the mend. After missing Games 2 and 3 with an ankle sprain, Hauser was upgraded to questionable for Game 4.

“He’s getting there,” Mazzulla said Sunday. He’s getting better. He’s day to day, getting better every day, so just got to continue that process. He’s a little bit better today than he was yesterday, and he’s just got to continue to work to get there.”

Getting Hauser back would add extra scoring punch to Boston’s bench, though he’s been quiet so far this postseason. After leading the Celtics in 3-point shooting percentage during the regular season (41.6%), the reserve wing has totaled just 16 points (on 6-of-13 shooting) across six playoff appearances.

Hauser was the only player listed on the Celtics’ latest injury report. Kristaps Porzingis was not as he continues to battle recurring symptoms from the viral illness he first contracted in late February.

Porzingis, who came off the bench in Games 2 and 3 and is averaging just 15.3 minutes per game in this series, addressed his limitations in an Instagram post Sunday, writing: “thankful for all the support people. onwards and upwards.”