With a win in their second game, they would achieve a feat that has eluded them for more than a decade.
After a promising opener, the Knicks look to start a season with consecutive wins for the first time since 1999 on Wednesday night when they visit the Golden State Warriors, who will likely be without star guard Stephen Curry.
New York beat Boston 106-104 on Christmas after going 0-8 against the division rival Celtics last season, including a sweep in the first round of the playoffs.
"It's a long year, but this game was very important for us to get off to a great start," Stoudemire said.
Anthony scored 37 points and Stoudemire added 21, and the pair of All-Stars combined to shoot 18 for 28 from the field and 6 for 9 from 3-point range as the Knicks overcame a 10-point fourth-quarter deficit.
"Most importantly for us, as a new team, we showed something," Anthony said. "We came together as a team. Even when we got down, there wasn't no frowns. Nobody was down. Mentally everybody was still up about it, and we willed our way to this win."
Early-season wins have been hard to come by for the Knicks (1-0) in recent years. New York hasn't won its first two games since opening 3-0 in 1999-2000, also the last season it won a playoff series.
The Knicks could have an easier time getting their second victory with Curry expected to rest his injured right ankle. Curry, who missed eight games with ankle problems last season and reinjured his right ankle in the preseason, had 21 points, 10 assists and six steals before landing awkwardly again Monday against Chicago.
"It's frustrating that this keeps coming up," Curry said.
Curry's performance prior to the injury helped Golden State (1-1) bounce back from a season-opening loss with a 99-91 win over the Bulls, giving coach Mark Jackson his first career win.
"I talked to the guys afterwards, and it means something because I dreamt of this moment," said Jackson, a point guard from New York who was the league's Rookie of the Year with the Knicks in 1987-88. "I told the guys I just didn't see the guys in uniform, but I thank God it was them because of their commitment, their focus, and their dedication. I'm extremely proud of that group."
The Warriors, continuing a four-game homestand, went 26-15 at Oracle Arena last season and 10-31 on the road. They had won eight straight at home against the Knicks before falling 125-119 on Nov. 19, 2010, despite Monta Ellis' 40 points.
Anthony was still playing for Denver while New York split two meetings with Golden State last season. He averaged 34.0 points for the Nuggets in two games against the Warriors, and is 19-6 against them in his career.
Former Knicks forward David Lee scored 28 points and 10 rebounds in his first career game against New York last season.
The Knicks, though, fortified their interior defense by trading for Tyson Chandler in the offseason. The 7-foot-1 center blocked six shots in his New York debut.