Drury scored the deciding goal in the shootout to give New York a 4-3 win over Montreal on Tuesday.
Henrik Lundqvist, who made his 60th start of the season, stopped Andrei Kostitsyn on the Canadiens' first attempt after making 26 traditional saves. He was beaten by Alexei Kovalev and Andrei Markov as the Canadiens drew even twice in the shootout by converting each of their next two attempts.
"I was very disappointed to let in two out of three, but they're pretty skilled. You have to give them that," Lundqvist said. "When I came in here I thanked Drury right away. It was a big goal. We didn't have to come back for another round, and that's a huge point for us."
New York moved one point ahead of Montreal into sole possession of sixth place in a tightly contested Eastern Conference playoff race.
"We found a way," Rangers coach John Tortorella said. "Both teams I thought played hard and it could have gone either way, but we found a way to win it."
"We just played 65 minutes of playoff hockey," Antropov said. "It was up and down, it was a great feeling. The fans were the same as we played when I was in Toronto because these are both Original Six teams, so it's always a rivalry and a nice atmosphere."
Andrei Markov's goal with 4:53 remaining in the third drew Montreal even at 3.
Markov, who assisted on Kovalev's power-play goal late in the second, beat Lundqvist with a sharp-angled shot from deep in the left circle.
"It was a terrible goal to let in but it happens. I'm happy as a team we stayed cool and just kept going," Lundqvist said.
Maxim Lapierre also scored for Montreal, which fell to seventh in the East with 81 points, two ahead of eighth-place Carolina.
"It was a huge point gained, but a tough point lost," said Canadiens defenseman Mike Komisarek, who took out his frustration on a penalty box camera after he was called for slashing Sean Avery late in the second period. "We have to look at the battles we won, not the negative."
The Canadiens fell to 1-1-2 under general manager Bob Gainey, who moved behind the bench after firing coach Guy Carbonneau on March 9.
"We had guys who were working hard," Lapierre said. "I know we didn't get the two points, that's not a good thing, but we did get one big point that keeps us in the race."
The Rangers' NHL top-ranked penalty-killing unit was tested by a tripping call against Scott Gomez with 1:44 left in regulation.
"When they tied the game up, there was no panic," Tortorella said. "I think that's what you look for in a club -- especially this time of year -- is when you get up, don't get too excited, and when something bad happens or a goal is scored again, whatever it may be, just try to keep it on an even keel.
"I thought that the penalty kill in the last two minutes, it was key, and so everybody contributed and found a way to win a game."
Antropov scored for the third straight game 7:13 into the second to put New York up 1-0. The Russian forward beat Price during 4-on-4 play for his fourth goal in seven games since the Rangers acquired him from Toronto.
Kovalev, who returned after missing two games because of the flu, got Montreal even at 1 during a power play late in the second. The Canadiens took advantage of Lauri Korpikoski's delay of game penalty for putting the puck over the glass.
Kovalev, who had two stints with the Rangers, scored his 17th goal at 18:26. He snapped a one-timer from the right side of the net to put Markov's cross-ice pass inside the right post.
Zherdev gave New York its second one-goal lead at 5:32 when he took Gomez's drop pass and put a wrist shot past Price.
Lapierre tied it just 40 seconds later when he beat Lundqvist with a shot from the slot at 6:12.
Callahan extended his point streak to four games when he put a backhander through traffic 10:58 into the third.
Guillaume Latendresse assisted on Markov's goal after missing 19 games because of a shoulder injury.
- Lundqvist made 50 starts as a rookie in 2005-06, 69 in 2006-07, and 72 last season.
- Callahan has two goals and three assists during his streak.
- Avery ended a three-game goal streak. He had four goals over that stretch.
- The Canadiens had scored six goals in each of their previous three games against the Rangers.
- Montreal LW Alex Tanguay missed the game due to the flu.