A clearing attempt was thwarted by Ryan McDonagh who promptly sent Nash in all alone on Price.
The win snapped New York's six game losing streak at home in the Stanley Cup playoffs.
"We were able to put pucks in places where we could get it back", said Derek Stepan.
Jesper Fast made most of a turnover and was able to slip the puck under the legs of Carey Price to get the Rangers on the board and got the Garden rocking. "The guys know you've got to breathe, you've got to go out, you've got to play".
Shea Weber is known for one of the world's hardest slap shots, so when the Canadiens defenseman wound up from near the blue line late in Tuesday night's game, all of Madison Square Garden gasped.
Rangers goalie Henrik Lundqvist, coming off a playoff career-high 54 saves in Game 2, stopped 26 shots in this one.
Radulov, who got the overtime victor in Game 2 on Friday night after Tomas Plekanec tied it with 18 seconds left in regulation, has two goals and three assists in the past two games.
Buchnevich had eight goals and 20 points in 41 games, although his playing time diminished down the stretch when Glass became a lineup fixture.
And one minute later Paul Byron took the lead for the Canadiens at 2-1. How Price, and by extension the Canadiens' defense, weathers that storm in the first period could be an indicator of how this game goes.More news: Rondo guides Bulls to 2-0 lead over Celtics
A different third period from the Rangers proved to be the difference as instead of sitting back on a lead they continued to push for a third goal. Radulov earned his fourth assist of the series on the play.
Through much of the first two games and essentially all of Game 3, Montreal forced NY into neutral-zone dumps, most of which were cleared easily.
"I thought it was a real good road game", Julien said. That gave the Blueshirts a 2-1 lead they would take into the third period.
After spending Monday reiterating the importance of playing their brand of hockey, Game 4 was contested at the Rangers' breakneck pace. D Nick Holden was also in the lineup.
"We weren't great in Game 1". There's no reason to think the Rangers, if they can maintain this level of intensity and with Lundqvist strong, can't win two of the next three, if necessary. "Obviously we didn't pick a good time yesterday to have a very ordinary game, but tomorrow we've got an opportunity to make this series 2-2". Rick Nash scored a shorthanded goal in Game 3 versus Pittsburgh last season, and the Rangers had an extra attacker when Brady Skjei scored in the third period on Sunday. For the first time in franchise history, the Blue Jackets won a playoff game in regulation despite Jake Guentzel continuing his scorching hot run and pulling the Penguins to within a goal with 30 seconds left, leading to some anxious moments among the 19,000 at Nationwide Arena.
It was unquestionably the Rangers' best start to a game in this series, notching the first few scoring chances and rocking the Canadiens back on their heels and into second place in the race for loose pucks.
Patric Hornqvist, Ron Hainsey and Tom Kuhnhackl also scored for Pittsburgh, and Marc-Andre Fleury - pressed into service because of an injury to Matt Murray at the start of the series - had 29 saves.
He shielded the puck from the Rangers' Kevin Hayes and, with one hand on his stick, worked the puck around Lundqvist for his second goal of the series to make it 3-0.