St. Louis, set to attend his mother's funeral with his teammates Sunday, got the opening goal and
Lundqvist made 20 saves. He had not played a game in Montreal since allowing four goals on Jan. 15, 2012. His last win at Bell Centre was March 17, 2009.
It was Montreal's worst playoff defeat since losing 8-2 to Carolina in 2002.
Budaj was beaten on the first shot he faced, from the slot by McDonagh on a power play at 1:28.
The Canadiens then took a succession of penalties, including two minors and a misconduct to former Rangers forward
Montreal got one back while short-handed with 4:38 left in the game when Eller beat Lundqvist with a quick, high shot from the slot.
That St. Louis got the Rangers started was fitting. He became a rallying point for his team for playing a day after mother France's death as they erased a 3-1 series deficit to beat Pittsburgh in the second round.
The boost the Canadiens got from their rousing pregame ceremonies in the first two series wasn't there as the Rangers showed all the speed and intensity in the opening period, outshooting Montreal 12-6 and taking a 2-0 lead.
Dominic Moore jumped on a loose puck after
Moore was the playmaker again as he slid a pass in front of the net and the trailing Zuccarello was able to poke it into an open side as the Rangers beat Price twice on their first five shots.
Bourque took consecutive hooking calls late in the first period, but made up for it in the second as he went hard to the net, whacked at
That brought the 21,273 at the Bell Centre back to life, but they went quiet again as Stepan broke in alone on the left side and beat Price with a low shot at with 1:01 left.