The Canadiens had a 31-17 shots advantage, holding the Rangers to five in each of the first two periods.
"It's frustrating if you're only getting five shots and they're scoring two or three goals," said Price, who was rested for the third time this season in Thursday's road loss to the New York Islanders.
He extended his shutout streak to 132 minutes, 30 seconds -- including a 33-save effort in a 4-0 win over Carolina on Wednesday. It was his 14th NHL regular-season shutout.
"He's the backbone of our team, but we did do a good job of getting the puck out of our end," said Gionta, who made it 2-0 in the second and added Montreal's fourth goal in the third.
Rangers backup Martin Biron lost for the first time in four starts. He stopped 27 shots after entering with a 0.95 goals-against-average and .962 save percentage.
"Don't look at our goalie, I'll tell you that," Rangers coach John Tortorella said. "Our whole crew in front of him never had the puck and we were chasing the game. We never caught up to it."
New York, which had a seven-game winning spurt from Oct. 3-17, 2009, fell short of its longest streak since an eight-game run midway through the 1974-75 season.
Cole gave Montreal a 1-0 lead with his sixth goal of the season on a power play 3:45 in. He got behind Rangers defenseman Michael Del Zotto to chase down Yannick Weber's long lead pass off the boards before firing a wrist shot from the right faceoff dot into the top left corner.
Gionta appeared to catch Biron by surprise with a shot from the right side for his first goal of the game 8:12 into the second.
"I think it summed up kind of the night for everybody, just overthinking the play," Biron said. "He's by himself going down the wide angle, bad-angle shot and I was overthinking the short side instead of just playing your natural instinct. Sometimes you make it more complicated than it needs to be and you give him room that he shouldn't have otherwise."
Biron made a glove save early in the third to deny Gomez, a former Rangers forward whose regular-season goal drought reached 40 games.
Plekanec drove a slap shot from the point past Biron for the Canadiens' second power-play goal 7:05 into the third to increase the lead to 3-0.
Gomez set up Gionta a second time, and the Montreal captain scored his second of the game and seventh of the season at 13:47.
"Gomer made two great reads on them," Gionta said. "He worked hard. He was on the puck, doing the right things, and when he does that he's a great player."
It was only the third time this season that New York trailed going into the third period. ... The Rangers' longest winning streak is 10 games, set during the 1939-40 season and matched in 1972-73. ... Gionta's shot for his first goal of the game smashed a plastic buckle on Biron's right pad to pieces on its way into the net. ... Gomez scored his last goal against Biron in a 2-0 win over the Rangers on Feb. 5.
Copyright by STATS LLC and The Associated Press
Arena: Bell Centre Location: Montreal, Quebec
Referees: Stephane Auger, Dave Jackson Linesmen: Steve Barton, Jonny Murray
Attendance: 21,273 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Erik Cole (6)
(Power Play) Assists: Yannick Weber, Tomas Plekanec
Brian Gionta (6)
Assists: Scott Gomez, Raphael Diaz
Tomas Plekanec (5)
(Power Play) Assists: Erik Cole, Max Pacioretty
Brian Gionta (7)
Assists: Scott Gomez, Mike Cammalleri