Curry has struggled against his former team, including a scoreless outing in a loss here last month.
"I was thinking that I didn't want every game against Chicago to be a bad game, to be a losing game," he said.
And for once, it wasn't.
The Knicks trailed by 13 early in the fourth and were down 98-91 after Chicago's Joe Smith hit a turnaround jumper midway through the quarter. But they ended the game on a 14-2 run.
Stephon Marbury, who scored 18 points, hit two 3-pointers during that stretch, including one from the top of the key after a pass from Curry that made it 105-100 with 11 seconds left. That sealed the win for the Knicks, who are 2-13 on the road.
Smith led Chicago with 22 points and 12 rebounds. Ben Gordon scored 21 points, and Kirk Hinrich added 20 points and nine assists. But the Bulls couldn't hang on even though they had double-digit leads over one of the league's worst teams in each of the final three quarters.
"We kind of relaxed and let them back in the game," guard Chris Duhon said. "When you give a team like this confidence, they're going to keep coming after you."
The Knicks outscored the Bulls 28-12 in the fourth thanks to Curry.
The Chicago native scored nine points in the final quarter and hit 11 of 14 shots in the game while blocking four. Crawford scored 17 points in the first half, including New York's final nine, and the Knicks led 53-52 at the break after trailing by 11 in the second quarter.
That was only the first wild swing in this game.
Trailing by three early in the third, the Bulls scored 13 straight to grab a 67-57 lead. The Knicks called time, and Nate Robinson quickly hit a 3-pointer, but baskets by Smith and a spinning Tyrus Thomas in the lane boosted the lead to 71-60 midway through the period.
The lead shrunk to five, but Duhon's layup and Aaron Gray's put-back in the final minute made it 88-77. Gray's jumper early in the fourth made it a 13-point game.
But instead of a rout, there was a rally. A big one.
Crawford's fadeaway jumper tied it at 100 with 2:29 remaining, and David Lee's dunk gave the Knicks a 102-100 lead with 1:59 left. Thomas then charged into Curry with 1:15 to go, and Marbury hit that 3-pointer to clinch the victory.
"I'm getting back into the flow, getting my legs under me," Marbury said.
Crawford added: "Those were big shots [Marbury] hit. It's tough because we have so many guys who can score, guys get frustrated when they don't get the ball. But Steph never did tonight and he stepped up and hit some big shots."
So did Curry.
"Three things are going to happen when Eddy gets it," coach Isiah Thomas said. "For us, we're going to get a high percentage shot. He's going to get us to the foul line, and hopefully, he won't make a turnover when passing it out of the double team."
Bulls fans booed loudly as their team walked off the court, a familiar chorus during this disappointing season.
Chicago's Luol Deng missed his second straight game with left Achilles tendinitis, so the Bulls turned again to Andres Nocioni -- not that he was a picture of good health.
Bothered by flu-like symptoms, he hit just three of 12 shots and finished with seven points after scoring 26 in Saturday's win over Sacramento.
Deng's absence and Nocioni's illness had little to do with this loss, though.
"We've got to figure out how to execute down the stretch," Smith said. "I think that's what it boils down to. Our execution down the stretch."
Bulls interim coach Jim Boylan said he hopes Deng, averaging 17.9 points, plays Friday at Philadelphia. Although his condition is improving, Deng wasn't sure he would be ready by then. ... The Bulls are 0-13 when an opponent scores 100 or more. ... The Knicks had lost six straight at the United Center. ... After initially giving Lee credit for a tip-in on a free throw by Curry with 2:25 left in the third, official scorers changed their minds in the final quarter. Instead, they gave Curry the point.