The Rangers erased a 2-0 deficit on goals by Paul Mara and Chris Drury. The tying tally came 46 seconds into the third period when Drury got to a rebound of Scott Gomez's shot and popped it over Drouin-Deslauriers, 20 seconds after New York's power play expired.
New York is 1-3-1 since a 10-2-1 start.
Erik Cole and Kyle Brodziak had the regulation goals for the Oilers.
Edmonton had chances to win it in overtime, using a power play and a pair of glaring turnovers in the Rangers zone to hold a 4-2 shots edge. Lundqvist finished with 29 saves.
Drouin-Deslauriers is 3-0 and has back-to-back victories on his resume, following a 37-save effort in a 2-1 win at New Jersey on Sunday.
Mara cut the Rangers' deficit in half during the second, when New York fired a season-high 20 shots. Ryan Callahan raced the puck up the middle of the ice and fed a pass to Mara, who zipped in a shot from the center of the left circle at 8:13. It was the defenseman's first goal in 66 games, dating to Nov. 6, 2007, at the New York Islanders.
The Oilers had increased their lead to 2-0 just 4:43 earlier, after they nearly scored shortly before on that shift. Brodziak and defenseman Sheldon Souray had a bit of a two-man break on Lundqvist, and Souray's shot was turned away at the right post.
Edmonton worked the puck back to the left point for a shot from Lubomir Visnovsky, whose drive was deftly deflected in flight by Brodziak for his second of the season.
Cole opened the scoring just 3:27 in when he steered a shot by Fernando Pisani past Lundqvist with his left skate. The play was reviewed and it was determined that Cole merely directed the puck in and didn't kick it.
The Rangers were less fortunate when the NHL went to the videotape to see if Callahan had scored the tying goal with 2:01 left in the second. Callahan took a pass in front from Markus Naslund, who was behind the Oilers net, and quickly sent the puck in on Drouin-Deslauriers.
The puck squeezed through his pads and kicked off his left skate, sending it trickling toward the goal line. Just before it crossed, the goalie smothered it with his blocker - obscuring the line from the camera's view.
Notes: The Oilers will play seven of eight on the road between Feb. 5 and Feb. 19. ... New York's previous high for shots in a period this season was 18, done three times. ... Edmonton's previous win at Madison Square Garden, came exactly five years earlier on Nov. 10, 2003 - a 5-4 victory. ... Drury was struck in the helmet by a shot from teammate Dan Girardi late in the third period. He appeared to be bleeding when he returned to the bench.
... Both teams had 13 shots and one full power-play chance in the third period.
