Henrik Lundqvist was perfect in the shootout and Brendan Shanahan scored the only goal in the tiebreaker for New York, which went into the All-Star break with a 2-1 win over Atlanta on Thursday night.
With the win, the Rangers completed a two-game home sweep of the Thrashers.
Leetch also announced that Adam Graves' No. 9 will also be retired.
"I'm glad we're retiring Gravy's number next season," Rangers coach Tom Renney said, "maybe we'll get nine [goals]."
Shanahan scored with the first shot of the shootout, and Mark Recchi, Slava Kozlov and Marian Hossa failed to solve Lundqvist. It gave the Rangers consecutive wins after a 2-6-2 skid and lifted them into an eighth-place tie in the Eastern Conference playoff race with the New York Islanders.
"Right now it's all about the wins," Lundqvist said. "I don't care if we play bad or if we play really good as long as we're winning."
It was fitting that defenseman Michal Rozsival scored the tying goal on the night the Rangers honored Leetch, the most prolific offensive defenseman in team history.
Brandon Dubinsky moved the puck from below the goal line to Nigel Dawes low in the right circle. He sent a crossing pass over to Rozsival, who scored his 12th of the season 8:52 into the third period.
New York nearly tied it moments earlier, but Johan Hedberg made a lunging stab with his glove to stop Brendan Shanahan's shot that seemed ticketed for the net.
Atlanta mustered only 18 shots through regulation after posting 14 in its 4-0 road loss to the Rangers on Tuesday night. The Thrashers didn't record a shot in overtime and dropped their fifth straight (0-4-1).
"We played a really solid game," Lundqvist said. "We didn't give up much and we played a patient game. That is the way we have to play."
Hossa staked Atlanta to a 1-0 lead in the opening minute of the second.
Hedberg got the start over Kari Lehtonen, who made 35 saves against the Rangers on Tuesday. In 10 previous games against New York, Hedberg was 7-3 with a 1.89 goals-against average.
He finished with 32 saves.
"The way we've been playing, we knew we had a lot of things to work on," Hedberg said. "We tried to play a smart team game. We didn't generate the final scoring chances, but I thought we played better defensively."
The Thrashers were again without leading scorer Ilya Kovalchuk, who served his one-game suspension for checking Rozsival hard into the boards in the first period Tuesday that got him kicked out of that game.
After the Rangers failed on four power-play chances in the first period, including a two-man advantage for 1:52, the Thrashers cashed in on their first 45 seconds into the middle period.
Atlanta started the period on the power play after Chris Drury was called for hooking with 8 seconds left in the first. Recchi moved the puck at the blue line to rookie defenseman Tobias Enstrom, who ripped a shot that found its way between Lundqvist's pads.
The puck trickled free in the crease behind Lundqvist, and Hossa easily smacked it the rest of the way in for his 22nd goal. Recchi's assist was his 101st point against the Rangers in 100 career games.
"We battled pretty good," Thrashers coach Don Waddell said. "We weren't worried about the shots, we just wanted to be patient and wait for our chances but do a good job shutting them down."
New York was 0-for-5 on the power play, stretching its man-advantage slump to two goals in 38 chances.
The Rangers lost to Minnesota on Feb. 4, 2004, when Richter's No. 35 was retired and beat Edmonton in overtime on Jan. 12, 2006, when Messier's No. 11 went to the Madison Square Garden rafters. ... D Marek Malik was sent home from practice Thursday morning for an undisclosed reason. Rangers coach Tom Renney said it was an "internal issue," declining to offer any details except to say that the struggling defenseman had not been traded. ... Thrashers C Jim Slater returned to the lineup after missing 13 games due to a lower body injury. ... Atlanta D Ken Klee took a puck to the face in the third period, leaving a trail of blood on the ice as he skating toward the dressing room. Klee didn't break any bones.