Now, even late deficits on the road don't rattle these Rangers.
New York improved to 6-0 on the season against the Devils and closed within four points of New Jersey, the leader in the Atlantic Division and Eastern Conference.
"We're going to have to beat them sooner or later," said Devils forward Zach Parise, who missed on the final shot of the shootout. "They've gotten a little closer than we'd like them to be. They really played well and limited our chances."
The Rangers appeared to have no chance to dent Brodeur, who was sharp in making 20 saves and was in line for his 97th NHL shutout.
He faced only mild pressure from the Rangers, who rarely got quality scoring chances. Many drives came from sharp angles or were blocked well before they could get in on goal.
Just 18 seconds after the Rangers' fourth failed power play expired, Drury tied it. Ryan Callahan swooped out from behind the net and fed a pretty left-to-right pass that Drury buried behind Brodeur with 4:46 left.
"There wasn't a lot of space," Drury said. "It seems like anytime you get a shot, there are sticks or bodies in the way."
New York tied Ottawa in points in the Eastern Conference playoff race but is still in sixth place on the basis of one fewer win.
The Rangers have held the Devils to five goals this season and have beaten them three times after regulation. New York is 12-2-3 in its past 17 and has gone to shootouts in five of nine -- winning four.
Lundqvist credited Drury for getting the game that far.
"He just finds a way to be at the right place at the right time," said Lundqvist, who earned his 100th NHL victory Tuesday in a 5-2 home win over Pittsburgh. "He just gets sharper and sharper. You get a really good feeling when you see him out there."
The only blemish was Dainius Zubrus' power-play goal in the first period that looked as though it would be enough. New Jersey leads Montreal by one point in the race for the top playoff seed in the East.
"We're not in the playoffs yet, so every point that we get is closer to a playoff spot," Brodeur said. "Definitely we're happy about getting one point. We wish we could have two."
Working solely in the Rangers' zone during their first power play, the Devils grabbed the lead at 6:05. Mike Rupp played the puck behind the New York net and fed a quick pass in front to Zubrus, who cut from the right wing boards between a pair of defenders and one-timed a shot by Lundqvist.
That marked just the second time this season that the Devils held a lead over the Rangers.
Brodeur faced only five shots in the period and made his best save by swatting away Martin Straka's shot after the Rangers forward was sent in alone off a stretch pass from defenseman Michal Rozsival from the New York blue line.
The Rangers outshot the Devils 9-4 in the second and nearly scored with the help of some deflections. The first came when Brendan Shanahan's drive struck the leg of New Jersey defenseman Colin White, forcing Brodeur to make a diving save with his glove.
About four minutes later, Fedor Tyutin's drive hit Brodeur and then the post but stayed out.
Lundqvist only saw 10 shots through 40 minutes, despite New Jersey having three power plays.
Dawes has been quite a find in the shootout. After failing on his first attempt of the season with the Rangers, Dawes has scored on four of five opportunities -- including a pair of winners.
He got Brodeur this time with a sliding shot between the pads. It was a lucky one, according to the Devils goalie.
"Well, he missed the shot," he said. "He was going to shoot it, I think low blocker and it kind of hit and went off his heel low. My stick was off the ice because I was reading something else."
Dawes chuckled and politely disagreed.
"I might not have gotten as much on it as I wanted to, but my intention was to go 5-hole," Dawes said. "I wanted to try to get him to freeze a little bit, and I got him with a good fake. Then I wanted to get him as he was trying to reset."
Devils LW Patrik Elias, who missed Saturday's game at Colorado due to a knee injury, was out again because of an illness. D Bryce Salvador was also scratched due to an injury. ... Former Devils C Scott Gomez heard boos every time he touched the puck. It was his third game in New Jersey since signing with the archrival Rangers. ... New York was 0-for-4 on the power play and has connected just once in 23 chances over seven games. ... Dawes said he was 0-for-4 on shootouts at Hartford (AHL).