The Rangers snapped the Bruins' five-game winning streak.
"It shows a lot of character," said captain Drury, who won it in the fourth round with a shot between Tim Thomas' pads. "We talked about it after the second period. One shot cuts it in half."
It wasn't in hand for the Rangers until a video review showed Patrice Bergeron's shot in the last round hit Henrik Lundqvist's skate and then the post and didn't cross the line even though the red light flashed.
"I wasn't sure," Lundqvist said. "At first I thought I had it underneath me the entire time and then I saw the review and I saw it hit the post. I was a little surprised."
So was the rest of the Madison Square Garden crowd that erupted when it was announced that the puck stayed out. Dawes' shootout attempt also faced a review that showed no-goal.
None of that would've happened if not for the late heroics of Dawes and Naslund, who scored 5:12 apart. Dawes brought the Rangers within a goal with 6:05 left and Naslund tied it with only 52.9 seconds showing.
Dawes took a pass in the slot from Lauri Korpikoski and shot from one knee to beat Thomas. Then on a rush, Brandon Dubinsky zipped a pass from the right-wing boards to the left circle to Naslund, for the final-minute goal.
"We haven't gotten the starts we wanted in a few games, but we have been able to at least get one point in many of them and sometimes even two," Naslund said of the Rangers (13-5-2).
Defensemen Zdeno Chara and Dennis Wideman provided the offense for the Northeast Division-leading Bruins (10-3-4), who could have moved one point behind the Rangers in the race for the Eastern Conference lead, but dropped four back.
Thomas, who didn't play in Boston's 6-1 rout of Montreal on Thursday, has allowed six goals in four outings. The Bruins had seven shots after the second period - four in overtime.
"It wasn't like we blew up a five-goal lead," Chara said. "A two-goal lead is probably the worst lead in hockey. We played pretty well most of the game, and then at the end they we were putting a lot of pressure on us. We could've probably handled it a little bit better."
Chara put Boston ahead midway through the second, and Wideman doubled the lead less than 4 minutes later with a short-handed goal. The Bruins recorded seven shots in the frame, but got a pair past Lundqvist.
Phil Kessel took a perfect feed at the left post by Marc Savard and was stuffed by Lundqvist's pad. The puck slid into the left circle, where Chara glided in and put his hulking 6-foot-9 frame into a slap shot that got through at 8:44.
About 3 minutes later, the Rangers had a chance to respond during a power play, but the Bruins scored a short-handed goal.
Rangers defenseman Michal Rozsival, who heard boos from the home crowd, couldn't get control of the puck in his skates. Boston's Stephane Yelle did and sent Savard the other way.
Savard fed the puck to Wideman, who whistled a drive past Lundqvist with 7:35 left in the period. New York has allowed six short-handed goals, tied with Columbus for the most in the NHL.
The Bruins missed a chance for their third straight win over an Original Six team.
"We've got to be happy with (one point)," Wideman said. "If you would have told me at the start of this week, we were going to get five out of six against Chicago, New York and Montreal, I think we probably would have taken that."
The Rangers had a chance to rally earlier when they received two 5-on-3 advantages in about 2½ minutes. The first lasted 26 seconds and the other for 1:13. Those power plays produced only three shots.
In their 5-2 victory over New Jersey on Wednesday, the Rangers scored twice while on 5-on-3 advantages. New York was given five straight power plays against Boston.
