Jaromir Jagr had three assists and Matt Cullen added two more for the Rangers, who won for the fourth time in five games and ended Atlanta's four-game winning streak. The Rangers got off to a quick start by scoring on two of their first three shots in front of Atlanta's first sellout crowd (18,545) of the season.
First it was Nylander's 15-footer past Atlanta goaltender Kari Lehtonen. Jaromir Jagr and Martin Straka earned assists on Nylander's fifth goal.
New York made it 2-0 six minutes later on a power-play goal by Michal Rozsival, his second. Jagr and Nylander had assists as the Rangers scored on only their third shot.
The Rangers made it 3-0 with 5:32 left in the first period on Brendan Shanahan's 13th goal.
Atlanta scored late in the period on a power play when Vyacheslav Kozlov connected on a long slap shot, beating New York goalie Henrik Lundqvist with 2:49 left.
New York made it 4-1 midway in the second period on a goal by Petr Prucha, his fifth. Matt Cullen, who assisted on Shanahan's goal, added another assist.
Ilya Kovalchuk, who assisted on Kozlov's goal, knocked in his 14th with a power-play goal at 14:07 of the middle period, only 20 seconds after two Rangers were penalized and the Thrashers had a 5-on-3 advantage. Marian Hossa, who leads the league in scoring, assisted.
Nylander added his sixth goal on a power play at 8:55 of the third period with Jagr getting his third assist.
Notes: Nylander's first period goal was the quickest allowed by the Thrashers since they entered the league in 1999. On two occasions Atlanta had allowed a goal after 35 35 seconds. ... Atlanta leads the league in goals (69) and Hossa leads the league in scoring with 28 points on 13 goals and 15 assists. Teammate Ilya Kovalchuk was next with 26 points (14-12) tied with Jagr (5-21). ... The Rangers are 7-2 on the road.