Price appeared to injure his right leg early in the second when Kreider slid into him after shooting wide on a breakaway. Price remained in the game, but was pulled after giving up two goals late in the second.
Canadiens coach Michel Therrien said Price wasn't injured, and was replaced by Peter Budaj to start the third because the team was playing so poorly in front of him.
"It wasn't because of an injury," the coach said of the decision. "The fact that he didn't play in the third period was more to protect him than anything, because we were not sharp."
Bourque said the Canadiens must put the tough loss behind them and focus their attention on Monday's Game 2.
"Good thing it's a seven-game series and we have a chance to get back in it on Monday," Bourque said. "I think we had a little bit of an emotional letdown after the Boston series.
"We talked about that to going into the game. Obviously, it didn't click. We have to just forget about this game."
The Rangers scored seven goals in a playoff game for the first time since April 17, 2007, against Atlanta (7-0), and did it on the road in the postseason for the first time since an 8-3 win at Quebec on May 8, 1995.
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 Brandon Prust. Stepan scored and Nash broke his slump with his first in 15 playoff games this year.
"We're all happy to see Nasher score because he's taken a lot of heat," Richards said. "That's a little weight off his back.
"We won the game. When you're in the playoffs, when it's 7-1, no one's jumping up and down about who scored goals."
Montreal closed the scoring with Eller's short-handed goal with 4:38 left.
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 Michael Bournival partially blocked a point shot and slipped a pass to a wide open St. Louis at the doorstep to open the scoring.
Moore was the playmaker again as he slid a pass in front of the net, and the trailing Zuccarello poked 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 Brian Gionta's pass, and saw it go in off McDonagh's stick at 12:38.
The crowd came to life but was quieted again when Stepan broke in alone and beat Price with 1:01 left.
With 12 seconds remaining in the period, Zuccarello made a reverse pass that had Price out of position for Richards to score into an open side.
NOTES: Rangers center Derick Brassard left the game early in the first period with an injury after a hit from Mike Weaver and didn't return. Vigneault said he is day to day. ... The Rangers went 3 for 7 on the power play after scoring only three times in 29 opportunities over their first 14 playoff games.
Information from The Associated Press was used in this report.