Jayson Tatum committed eight turnovers but finished with 25 points and 10 rebounds. Marcus Smart added 17 points, 14 in the fourth quarter, and nine assists for the Celtics, who have won three of four.
Brown said he and Tatum talked before the game about not dwelling on Tuesday's 10-point loss to Philadelphia.
''I just needed to be Jaylen. And our team played great tonight,'' Brown said.
Brown and Tatum followed the jolt provided by Tristan Thompson, who had seven points, eight rebounds and three blocks in his return after missing 12 games due to the league's health and safety protocols. Coach Brad Stevens was pleased with his team's consistently physical play.
''That was what we're used to - kind of a grind-out Celtic win, which is what we've been about when we're at our best,'' Stevens said.
''We're fine,'' Randle said. ''We're not going to get much out of frustration. We've got to figure out what the problem is and figure out how to solve it.''
New York and Boston entered the day tied for seventh place in the Eastern Conference playoff race. The game was tight throughout, featuring eight ties and 17 lead changes.
The Celtics trailed by seven early in the fourth quarter before using a 7-0 run to edge in front 87-85.
It was 91-88 when Tatum had a pass intercepted, leading to a dunk on the other end by Randle.
Smart missed a 3 and New York looked to take the lead, but Barrett had his pass picked off by Grant Williams, leading to a layup by Brown that made it 93-90 with 1:02 remaining.
Barrett tied it with a 3-pointer and Smart answered with a 3 of his own. Alec Burks came up short on step-back 3, and the Celtics closed it out from the free-throw line.
Thompson brought some toughness to the rotation by keeping plays alive, attacking the paint and getting to the foul line early. He had seven points, five rebounds and a block in 11 minutes of action in the first half.
Turnovers were an issue for the Boston for the second straight game. The Celtics turned it over 20 times, leading to 21 New York points.
Barrett was the most active for the Knicks at the outset, hitting all three of his attempts beyond the arc and scoring 16 points in the first half.
Coach Tom Thibodeau said he expects the second-year guard to be even more important down the stretch.
''There's still a lot of room for growth and a lot of work that needs to go into it. But I like his approach from the summer,'' Thibodeau said. ''I'm very pleased with his overall progress and I think he'll continue to grow.''
Knicks: Opened the second half with an 11-3 run. . Were 8 of 16 from the 3-point line in the opening 24 minutes. . John Henson (strained right calf) and Mitchell Robinson (right foot surgery) were out.
Celtics: Led 47-46 at the half. . Started 2-for-10 from the field. . Romeo Langford made his first start of the season and the third of his career. . Kemba Walker (left knee injury management) and Evan Fournier (health and safety protocols) sat out.
The Celtics shot 42% (36 of 86) from the field. Boston had lost the previous 12 games in which it shot less than 45%.
Knicks: Host Memphis on Friday.
Celtics: Host Minnesota on Friday.
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