Drury scored 11 seconds after Chicago's Andrew Ladd was sent off for slashing.
Brandon Dubinsky also scored, and Henrik Lundqvist made 32 saves to help the Rangers win their third straight game. Atlantic Division-leading New York is 11-4 in overtime and shootouts and 17-8 in one-goal games.
"As many close games as we do, you learn to win games like that," Drury said. "It's like we've done it night-in, night-out."
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.
Asked if the two points were the Rangers' hardest-earned this season, New York coach Tom Renney said, "Yeah, and maybe so far the most satisfying."
New York improved its penalty killing rate to 88 percent, second best in the NHL and just behind Minnesota.
"It was a weird one, strange, tough with the amount of penalties." Dubinsky said. "Not wanting to say something about the officiating, our penalty killing did a great job and Henrik was sharp."
Lundqvist was impressed with his teammates short-handed work.
"They [the Blackhawks] have a couple of skilled guys," Lundqvist said. "We were aggressive blocking shots. We didn't give them too much time."
The goalie was less enthusiastic about referees Mike Hasenfratz and Dean Morton.
"I don't think we played that rough," Lundqvist said. "But calling everything? I think they're destroying the game for both teams."
In the end, however, Ladd's overtime infraction set the stage for the Rangers. New York entered the game with the NHL's fourth-worst power-play conversion rate -- 14.3 percent -- but went 2-for-6 with the advantage on Friday to pull out the victory.
"We were down 2-1 and you can't take that penalty in overtime," Chicago coach Joel Quenneville said. "Tonight's loss was frustrating considering the number of chances we had.
"To score only one [power-play] goal after having so many power-play is very unsettling, but you have to give credit to New York's penalty kill."
Chicago's Brent Seabrook tied it at 2 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.
Added Chicago's Brian Campbell: "We're fortunate to get a point tonight. The power plays obviously have to be better."
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 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.
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.