Skating 4-on-3 in the OT after Boston was whistled for too many men on the ice, Zuccarello beat Rask with a rising shot from the right circle to lift the Rangers to their ninth win in 13 games overall (9-3-1) and their seventh straight against the Bruins.
"It's such a quick release," said Lundqvist, who made 33 saves playing on back-to-back days. "Every team has one or two players that can snap the puck like that. As a goalie, you just have to be on your toes at all times.
"It's hard. He fakes it. Looks you off and it comes at you real fast."
Rangers coach Alain Vigneault treated this one like an important game, going to Lundqvist again.
"Like I said before, it was a big game and Henrik had been playing real well," he said. "I just thought it was the right thing to do."
Bruins coach Bruce Cassidy thought the penalty in OT was the correct call.
"It was all three of them. Sometimes you try to gain an advantage and get away with it." he said. "I can't complain about it. It's a lousy way to lose."
Trailing 2-1, the Bruins tied it on Marchand's power-play goal at 5:38 of the third period. Marchand one-timed a cross-ice pass from David Pastrnak from the right circle for his 13th. Boston got the power play after Marchand drew a holding penalty on David Desharnais.
"There was a period where we weren't at our best, but we battled back," Rask said.
Boston's David Krejci hit a post with seven minutes left in regulation.
The Rangers took a 1-0 lead when Grabner benefited from a fluky bounce with 5:18 left in the first. He fired a shot from the slot that sailed over the net, but the puck caromed off the glass and hit Rask's back before sliding into the net for Grabner's team-leading 16th goal.
New York made it 2-0 on Miller's power-play goal 2:41 into the second. With Krejci off for high-sticking, Miller collected Ryan McDonagh's pass near Boston's blue line at full speed, cut into the zone, shifted around defenseman Brandon Carlo and lifted a backhander behind Rask.
Rask kept it a two-goal game by making a nice right-pad stop on Rick Nash's clean breakaway while the Bruins were on a power play.
Heinen then sliced Boston's deficit in half by tipping Zdeno Chara's snap shot between Lundqvist's pads with 2:48 left in the second.
Boston had a goal taken off the board early in the opening period by a coach's challenge because the play ended up being offside. Ryan Spooner had redirected Torey Krug's pass into the net 4:39 into the game.
There was a large contingent of Rangers fans wearing blue jerseys sprinkled throughout the stands, especially in the lower seats. They broke into chants of `Let's Go Rangers!' a handful of times.
They broke into a loud roar on the game-winner. Some remained and were still cheering minutes after the building was nearly empty.
Lundqvist also made 33 stops in a victory at home against Los Angeles on Friday night. ... Marchand has at least a point in all eight games since returning after missing six in a row with an undisclosed injury. ... Spooner was moved up to the second line with struggling LW Anders Bjork out as a healthy scratch. ... Boston players entered TD Garden wearing Holiday outfits. ... It was the only regular season meeting in Boston between the teams this season. They play at Madison Square Garden on Feb. 7. New York won the previous game -- 4-2 at home on Nov. 8.
Rangers: Host Anaheim on Tuesday in the teams' first meeting this season.
Bruins: Host Columbus on Monday, ending a stretch of five of six at home.