The Thrashers have 86 points to strengthen their hold on third place in the Eastern Conference. Atlanta, which began the night with a two-point lead over Tampa Bay in the Southeast Division, took just 20 shots in regulation, but backup goaltender Johan Hedberg stopped 38 of the 39 he faced, including one in overtime.
Matt Cullen's holding penalty gave Atlanta the one-man advantage 1:31 into the extra period.
The Rangers, who had gone 3-1-1 in their last five games, are among five teams chasing the final two playoff spots in the East. Carolina and the New York Islanders are tied for seventh with 78 points, and the Rangers pulled into a tie with Toronto for ninth one point back. Montreal is in 10th with 76 points.
New York had Blair Betts, Michal Rozsival and Marek Malik trying to buffer Henrik Lundqvist when Zhitnik fired from the point to sail the puck under the goalie's right pads.
Sean Avery's 13th goal gave the Rangers a 1-0 lead with 53 seconds left in the first. Michael Nylander, credited with his 49th assist, passed from the goal line to the right circle, where Avery used a wrister to beat Johan Hedberg.
Marian Hossa, who had an 11-game points streak snapped in a
3-2 loss at Philadelphia on Thursday, tied the game 2:51 into the second. With Ilya Kovalchuk storming from the penalty box and trying a slap shot from the right circle, Hossa deflected the puck past Lundqvist's glove side for his 41st goal.
Hedberg, making his first start since Feb. 22 to give Kari Lehtonen the night off, improved to 7-4-2.
Lundqvist dropped to 29-22-6 after making 20 saves.
Notes: Before Zhitnik scored, the Rangers had killed 98 of their last 110 penalties over the last 28 games for an 89.1 percentage. ... Atlanta has killed 51 of its last 57 penalties over the last 13 games. ... The injury-depleted Rangers survived a scare midway through the first when Kovalchuk accidentally hit Rozsival in the jaw with his stick. Rozsival fell face-first to the ice and needed a couple of minutes before he could skate to the bench. He returned, however, and finished with a team-high ice time of 30:47.