Brad Marchand, whose overtime goal won the opener, and Milan Lucic stretched the Bruins' lead in the final period.
Milan Lucic and Dennis Seidenberg each had a pair of assists for Boston.
"To start off, 'Dobi' made some huge saves for us, especially early in the first period, " Bruins forward Milan Lucic said.
Notwithstanding Lucic's goal, Toronto goalie James Reimer's looked unbeatable in net, narrowly missing a shutout after stopping 30 shots for the win.
Li, who reached the final of the Australian Open in January, beat Croatia's Mirjana Lucic-Baroni 6-1 6-2 in their second round match.
"Another New York-Boston series, " Bruins forward Milan Lucic said after Monday night's 5-4 overtime win over the Toronto Maple Leafs in Game 7.
He skated into the New York end and gave the puck to David Krejci, who was stopped by Lundqvist, but Lucic converted the rebound.
"We expected the crowd to be energized and obviously there was a lot of emotions going into this game, " said Bruins forward Milan Lucic.
Rangers, Stralman 1, 2:07. 4, Boston, Krejci 4 (Lucic, Seidenberg), 8:44. 5, Boston, Horton 4 (Lucic, Ference), 18:29. 6, Boston, Marchand 7 (Bergeron, Seidenberg), 19:17.
Zeljko Lucic let loose a fierce and pained baritone as Rigoletto, combining with Damrau for an unforgettable second-act duet filled with emotion, inflection and even tears.
Tortorella compared Staal's importance to the Rangers to that of hulking defenseman Zdeno Chara's to Boston, and called Clowe New York's version of Bruins hard-hitter Milan Lucic.
Milan Lucic had a poor season but was solid in the playoffs and scored the goal that cut the deficit to 4-3 with 1:22 left in regulation.
Marchand made it 4-2 with just 26 seconds gone in the third period, Milan Lucic scored at 12:39 and the Bruins worked hard the rest of the way.
Horton's scoring play started when Krejci brought the puck out of his own zone and passed it to Milan Lucic, who carried it over the left side of the Devils' blue line.
Boston came within one after pulling Tuukka Rask from net in the dying seconds of the third that allowed Milan Lucic to score in front of the Toronto net from a deft pass from future Hall of Famer Jaromir Jagr.
Lucic passed it to Krejci in the middle and he immediately passed it to Horton, who shot a 20-footer from the right past Hedberg, playing for the first time this season after Martin Brodeur started the Devils' other four games.
While injured Bruins defensemen Dennis Seidenberg and Wade Redden continue to practice and move closer to returning, the Rangers are dealing with the loss of defenseman Anton Stralman, who got hurt when he was checked hard Tuesday night by Milan Lucic and left the game in the second period.
Brad Marchand and Milan Lucic scored in the final period after Johnny Boychuk broke a tie in the second, Lundqvist gave up more than four goals for the first time in 152 games, and Boston beat New York 5-2 on Sunday to take a 2-0 lead in the Eastern Conference semifinal series.
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