New York has lost six straight, the club's longest streak since it dropped seven straight from Dec. 16-29, 2006. The Thrashers, who had dropped 11 of their last 13, earned just their third regulation victory in 22 games.
"That was big for us because they are ahead of us in the standings," Kane said. "They got no points, and we got two."
Stewart scored his 14th goal in the first for Atlanta, and Marc Staal followed with his seventh goal for New York in the second. Brandon Dubinsky's 19th gave the Rangers a 2-1 lead early in third before Kane scored twice, the go-ahead goal on a power play with 2:20 remaining.
Kane's second goal, his 16th of the season, came after New York goaltender Henrik Lundqvist stopped Dustin Byfuglien's slap shot and a wrister from the slot by Kane, who quickly controlled the puck on the right side and lifted it into the net.
"He made some big saves, but we kept making shots," Kane said. "He played well, but we found a way to get pucks by him."
Lundqvist, who watched from the bench the last two games, was in goal for the first time since getting pulled Feb. 3, when he allowed three goals on 12 shots in a 3-2 home loss to New Jersey. The All-Star goalie was 1-3-1 with a 3.39 goals-against average in his last five starts, but 13-6-2 with a 1.76 GAA in the previous 21 games.
"It seemed like they always made good rebounds," Lundqvist said. "They were always around the net. We're angry, disappointed and frustrated. We have to angle it from something positive and get energy from it."
Stewart essentially erased his 14th goal, which gave the Thrashers a 1-0 lead 11:08 into the first, with a hooking penalty in the first minute of the second.
Staal, who drew the penalty, made it 1-1 with a wrister off a rebound moments later.
"We were going pretty good, and then a few mistakes cost us the game," Staal said. "Those were two big points we wanted very much."
Thrashers defenseman Johnny Oduya set up Stewart's goal by checking Matt Gilroy into the boards. Alex Burmistrov controlled the puck through the neutral zone and fed Stewart down the left side for a backhander 11:08 into the first.
Dubinsky scored his fifth goal and 14th point in his last 17 games. He was skating inside the left circle when he took Marian Gaborik's backhanded pass and beat Ondrej Pavelec.
Gaborik, who missed a penalty shot with 12:24 remaining, assisted on both goals and now has 12 points, including 11 assists, in his last 10 games.
Gaborik was awarded the penalty shot after Atlanta defenseman Brent Sopel hooked him from behind to stop his shorthanded breakaway attempt. Pavelec stopped Gaborik's wrister by dropping to stop the puck with his right leg pad.
"It was time to do something," Pavelec said. "It was time to step up, and I made a save for the guys. After that, I believed we were going to score some goals and win the game. It's a big win for us."
Thrashers coach Craig Ramsay credited Kane with heeding advice from the bench after Atlanta fell behind 2-1.
"I said to him that I needed him to go out and win some battles and keep the puck," Ramsay said. "He was just ready to go. He was ready to try. We had to shorten up our bench, so he was going and going. There were certainly a lot of guys that stepped up tonight, but for him to bang in a couple was pretty darn important."
New York C Vinny Prospal, playing in his fourth game after missing 53 with a knee injury, earned his first assist on Staal's goal. ... Thrashers D Tobias Enstrom had one shot on goal and blocked a shot in 26 shifts after getting activated from injured reserve. He missed six games with a broken finger. ... Atlanta LW Eric Boulton and New York LW Brandon Prust served 5-minute fighting majors 6:07 into the first. Each team missed its only shot during the stretch.
Copyright by STATS LLC and The Associated Press
Arena: Philips Arena Location: Atlanta, Georgia
Referees: Frederick L'Ecuyer, Brad Watson Linesmen: Darren Gibbs, Derek Amell
Attendance: 15,093 (81.4% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Anthony Stewart (14)
Assists: Alex Burmistrov, Evander Kane
Marc Staal (7)
(Power Play) Assists: Marian Gaborik, Vinny Prospal
Brandon Dubinsky (19)
Assists: Marian Gaborik, Ryan McDonagh
Evander Kane (15)
Assists: Anthony Stewart, Ron Hainsey
Evander Kane (16)
(Power Play) Assists: Dustin Byfuglien, Tobias Enstrom