The Thrashers, in their seventh NHL season, were playing their first postseason game. They desperately tried for a tying goal in the final minute on the power play but were denied.
With the tight victory in the Eastern Conference quarter-final game, the Rangers won for the first time since the 1997 playoffs. They were swept by New Jersey in the first round last year, but Jaromir Jagr helped make sure New York enjoyed a better start in this series. The Rangers outshot the Thrashers 38-24.
The Rangers drew only two penalties in the game, including one against Thomas Pock for holding the stick with 1:11 to play. Atlanta pulled goalie Kari Lehtonen after the penalty, but was stymied by Henrik Lundqvist, who stopped 35 shots.
Jagr got his 68th playoff goal. Michael Nylander had a goal and two assists while Michal Rozsival and Marcel Hossa also scored for the Rangers.
Eric Belanger, Shane Hnidy and Pascal Dupuis replied for Atlanta.
The Thrashers cut New York's lead to 4-3 about six minutes into the third period when Dupuis scored from in front of the net. But the Rangers held on.
Nylander set up the first goal of the series with a cross-ice pass to Jagr, who blasted a shot past Lehtonen.
There were no penalties until late in the first and each team scored quickly on its first power-play opportunity.
Rozsival scored only 16 seconds after a holding penalty on Andy Sutton to push the Rangers' lead to 2-0. But Rozsival was called for hooking late in the period and Belanger scored just 19 seconds later.
Hossa, often working against his brother, Atlanta's Marian Hossa, pushed the lead to 3-1 with a goal midway through the second.
Hnidy countered for Atlanta, but the Rangers quickly took another two-goal lead. Lehtonen blocked a shot on a 2-on-1 break, but Nylander scored on the deflection off Lehtonen's glove for a 4-2 lead.
Notes: Dupuis was down on the ice for a few minutes late in the opening period after he was sent crashing into the boards. ... Rangers D Karel Rachunek was not in uniform as he continues to recover from a sprained knee. He may return next week. ... Atlanta resident and former heavyweight boxing champion Evander Holyfield attended the game. ... The last playoff game in Atlanta was in 1980, when the Flames lost to the Rangers before moving to Calgary later in the year.