With the victory, the Rangers snapped the Bruins' five-game winning streak.
It wasn't in hand for the Rangers until a video review showed Patrice Bergeron's shot in the last round hit the post and didn't cross the line even though the red light flashed. Dawes' attempt in the tiebreaker also faced a review to show that 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 against Tim Thomas.
Dawes made it 2-1 with 6:05 left, taking a pass in the slot from Lauri Korpikoski and shooting from one knee to beat Thomas. Then on a rush in the closing minute, Brandon Dubinsky zipped a pass from the right-wing boards to the left circle to Naslund, who scored with 52.9 seconds remaining.
Defensemen Zdeno Chara and Dennis Wideman provided the offense for the Bruins, 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.
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 goalie Henrik 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.
Still, the Rangers had a chance to get back in it when they received the first of two consecutive 5-on-3 advantages in a span of about 2 1/2 minutes. The first lasted 26 seconds and the other went on for 1:13. The two-man power plays produced only three shots. New York was given five straight power plays against Boston.
Notes: Bruins D Andrew Ference sat out due to a foot injury sustained Thursday against Montreal. Rangers C Scott Gomez (leg) missed his second straight. ... There was a brief delay in the second period after linesman Pierre Champoux fell backward during a stoppage in play and hit his head. He was treated for a cut on the bridge of his nose and remained in the game. ... Wideman's goal was the first for the Bruins while short-handed this season.