Douglas scored a career-high 30 points, and New York made 16 of 24 3-point attempts in a 120-112 victory over the Chicago Bulls on Thursday.
It was an outstanding shooting display for the Knicks after they hit just 29.1 percent over the first three games.
Leading the charge was Douglas, who made 5 of 9 from long range.
"I make sure that every time I shoot it that I have confidence that it's going in," he said. "I can miss 10 in a row. I'm going to shoot the next one and make it."
Douglas had plenty of help in a game when his teammates seemed as locked in as he was.
Danilo Gallinari hit four 3s without a miss and finished with 24 points -- all but three in the first half as the Knicks took a 21-point lead in going up 70-52 at halftime.
Raymond Felton was 4 of 6 from long range and finished with 20 points and 10 assists, while Amare Stoudemire added 14 points and eight rebounds. The Knicks forced 20 turnovers and got a reprieve after a dramatic first week.
Besides close losses to Boston and Portland after taking the opener from Toronto, they had to postpone Tuesday's home game against Orlando because of an asbestos scare at Madison Square Garden.
They overcame another big effort from Chicago's Derrick Rose, who scored 24 points and had 14 assists, but he sat out the final 9:31. That didn't sit well with fans who chanted "We want Rose!" in the closing minutes as the Bulls made one final push.
"Once you start to see the ball going in from different people it makes it a lot easier for everyone else," Knicks coach Mike D'Antoni said.
The Bulls were trailing by 17 points before making a run late in the third, cutting it to 10 on a 3-pointer by Deng with 28 seconds left, They were within 95-87 after a 3 by Korver early in the fourth. The Knicks responded by scoring 10 straight points with Ronny Turiaf's three-point play on a dunk with 9:31 left capping that spurt.
That's when Rose and Deng headed to the sideline and joined Joakim Noah, who did not play at all in the fourth quarter. Fans made it clear who they wanted on the court, but coach Tom Thibodeau didn't budge, sticking with a group that chipped away but ultimately came up short.
"The second unit I thought fought hard to close it, and I wanted to see what they could get out of it," Thibodeau said. "They were closing a lot harder to the 3-point line. The way their guards were shooting, I thought the energy to get out to the line was [what we needed]. New York does a great job of running pick-and-rolls. They roll hard to the rim. You've got to pull in, but then you've got to get out to that line. You use a lot of energy doing that. I thought about it, but I thought the group that was out there was covering the line pretty well."
Rose was not available for comment afterward, but Deng said it was the right decision to make.
"That group that came in did a better job than us," he said.
Rose apologized for missing a scheduled taping of CBS' "The Good Wife" in New York on Tuesday. He was scheduled to fly in for the day, but he said he overslept after the Bulls played Portland the previous night. "I'm happy it's out of the way," Rose said. "I talked to the producer today, just apologized to him. He said that he felt that it really wasn't anything that big. ... I'm not that type of guy where I'll try to big-time anyone or anything. It's not in my character as a person and I'm sorry I did it." ... Thibodeau wasn't about to wax nostalgic over going against former boss Doc Rivers when the Bulls visit Boston on Friday. "I'm not really thinking about Boston right now," he said. Thibodeau spent three seasons as an assistant in Boston before taking the Bulls' job in the offseason. ... This was the Knicks' first game on TNT since Nov. 29, 2007, when they got crushed 104-59 by Boston.