New York has won five games in a row after falling behind 3-1 in its semifinal set against Pittsburgh and holds a 2-0 lead in this best-of-seven set heading back to New York.
The next two games will be played in the Big Apple, with Game 3 set for Thursday night.
Montreal will have to overcome the serious deficit without starting goaltender Carey Price, who went down with an injury in Game 1 and will miss the rest of the series.
Taking his place in net was Dustin Tokarski, who had played in three games earlier in the season. He allowed all three goals on 30 shots in his playoff debut.
Max Pacioretty scored for Montreal.
The Canadiens came storming out of the gates in an effort to take an early lead, but Lundqvist was sharp as he stopped Rene Bourque down low twice in the first minute, then fought off a Brendan Gallagher one-timer three minutes in during 4-on-4 play.
Montreal, though, finally got one through at 6:14 as Mats Zuccarello lost the puck in his skates in front of the net and Lundqvist tried to poke it out of danger, but it hit off Pacioretty and went in for his fourth goal of the playoffs.
It took just 17 seconds for the Rangers to answer, however, as McDonagh threw the puck on net from the left point and it hit off Josh Gorges in front before going into the net to tie the game.
Lundqvist again came up big off a turnover as Montreal used a pair of passes to give Andrei Markov a clear shot in the slot, but he turned it away with around four minutes left in the opening frame.
New York then grabbed a 2-1 lead with 1:02 left in the first as a rush play into the Montreal end saw Derek Stepan pass the puck from the slot to the left wing for Chris Kreider, who one-touched it over to the right wing and Nash one-timed it home for his second goal in as many games.
The only goal of the second period went to New York, as the team was awarded a power play after Alex Galchenyuk was called for tripping at 7:29.
Holding the puck in the high slot, McDonagh sent the disc to the left side where Stepan fed it back to the slot and St. Louis' one-timer went into the right corner of the net for a 3-1 advantage at 8:03.
Lundqvist stopped eight shots in the frame, helping the team kill off a full power play and a late short-handed situation that carried over into the third.
Montreal continued to pepper Lundqvist in the third to try to get back into the game, but he turned away all 19 shots to keep the two-goal lead.
The Canadiens were awarded a power play with 4:30 left after Benoit Pouliot was called for boarding, and the team pulled Tokarski for a 6-on-4 advantage.
Lundqvist, though, made several saves during the advantage, including one on a P.K. Subban left-point shot with 2:43 to play and he swallowed the rebound shortly before the penalty expired.