Chicago's Brent Seabrook tied it on a 5-on-3 power play with 4:29 left in the third, firing a low shot from the top of the slot past Lundqvist.
Jonathan Toews also scored for Chicago, and Nikolai Khabibulin made 19 saves.
New York killed 10 of 11 Chicago power plays. Included in the kills were the first four of five 5-on-3s and a continuous Chicago manpower advantage lasting 5:45 late in the second set up by a series of four Rangers minor penalties.
New York entered the game with the NHL's second-best penalty-killing rate, 87.9 percent.
Toews scored the only goal of the first period, on a deflection with 4:32 left.
Parked in front of the crease, Toews tipped Kris Versteeg's shot from the top of the slot upward and just past Lundqvist on the glove side. Lundqvist tried to swipe the puck out, but it already had narrowly crossed the goal line.
The Rangers killed a 2-minute 5-on-3 Chicago power play at the end of the first. Martin Havlat fired a shot off the left post - the Blackhawks best chance during the advantage - as the power play ended.
Drury's 5-on-3 power-play goal tied it at 1 at 6:25 of the second. He ripped a one-time shot past Khabibulin from the left circle after taking a feed from Michal Rozsival.
The Blackhawks continuous power play lasting 5:45 last in the second included three 5-on-3 advantages, lasting 1:07, 50 seconds and 18 seconds.
The Rangers limited the Blackhawks during the entire advantage, permitting only a couple of tough chances that were handled by Lundqvist.
Dubinsky put New York ahead 2-1 by completing a two-on-one break with Lauri Korpikoski at 7:58 of the third. Korpikoski faked a shot, then passed to Dubinsky who scored with Khabibulin down and out of position.
Notes: Blackhawks D Duncan Keith sat out after suffering an undisclosed head injury from a hard, open-ice hit in Chicago's 4-1 win over Buffalo on Wednesday night. Keith, who leads the Blackhawks with nearly 26 minutes of ice time per game, is listed as day-to-day. ... Chicago RW Troy Brouwer was a healthy scratch for the third straight game. ... The Rangers reported no injuries, but LW Aaron Voros and C Dan Fritsche were healthy scratches. ...
The game was the Rangers' first in Chicago since a 2-1 OT loss on Dec. 5. ... The crowd of 22,624 was Chicago's 21st sellout in 21 home games this season.