Patrick Sharp and Johnny Oduya scored 62 3.
Patrick Kane's empty-net goal proved to be the game winner and Andrew Shaw also scored for the Blackhawks, who have won four of their last five games.
Chicago, which got 22 saves from Ray Emery, has 81 points and sits four points back of idle Nashville for the fifth spot in the Western Conference.
Brandon Prust, Brad Richards and Artem Anisimov all scored for the Rangers, who have dropped three straight for the first time since losing the first three games of the season.
Henrik Lundqvist was touched for three goals on 21 shots for New York, which sits atop the Eastern Conference with 91 points, four ahead of Pittsburgh.
With the Rangers holding a 2-1 lead, the Blackhawks tied the game off a nice play. Kane grabbed the puck at the right circle and sent it to the low right side where Marian Hossa was sitting. Hossa one-touched it over to the left and Sharp one-timed it home with 6:58 to play.
Just over a minute later, Oduya scored his first goal as a member of the Blackhawks when his big blast from the left point sailed past the glove of Lundqvist.
Kane then put the puck into the empty net with 53 seconds to play, but the Rangers got one back moments later when Richards shot home a bouncing puck from the slot.
The Rangers, though, were unable to net the equalizer and dropped their four straight road game.
New York struck with 47 seconds to play in the first as Anisimov got the puck behind the defense and was able to tuck the it past Emery.
Chicago got the only goal of the second period when Shaw's big blast from the left point trickled past Lundqvist with 5:32 left.
The Rangers made it a 2-1 game 7:11 into the third when Prust slammed home a rebound at the right side for his fifth of the season.
The Rangers open a seven-game homestand on Sunday against the Islanders...Chicago hosts Los Angeles on Sunday...The Blackhawks have won three of the past four against the Rangers.