Price's ninth career shutout was his first in 27 starts since Nov. 20, when he made 30 saves in a 3-0 win over Toronto. He took the NHL lead with 26 wins as Montreal won its third in a row since the All-Star break.
"It felt like a long time but wins are coming so these are secondary," said Price, who has started a league-high 46 games. "It seemed like today it was almost necessary. Our guys played really well defensively. We knew it could be a 1-0, 2-0 game."
Gomez, a former Rangers forward, made it 1-0 with 1:26 left in the second with his seventh goal. Tomas Plekanec scored his 18th into an empty net with 37.4 seconds remaining.
New York killed both of Montreal's power-play opportunities but the Rangers went 0 for 4 on their man-advantage chances.
"Our penalty killing was good, a lot of our game was good -- our power play was a bit of a letdown," Rangers coach John Tortorella said. "That's where you're looking at your 0-0, 1-0, whatever it may be. You need your power play to kick in."
The Canadiens, outshot 19-6 in the third period, held onto the lead and strengthened their position in the Eastern Conference playoff race. Montreal is in sixth place with 65 points, three ahead of the seventh-place Rangers with two games in hand. The Canadiens trail fifth-place Washington by one point.
"They're a good team," Tortorella said. "Obviously with the score, it could have gone either way. They end up scoring a goal, we don't capitalize on some chances, and our power play doesn't work. That's why they win tonight."
The Canadiens won despite the absence of defenseman James Wisniewski, who missed the game because of illness.
Alexandre Picard, who hadn't played in four weeks, took Wisniewski's spot in the lineup and earned an assist on Gomez's goal. Picard took Yannick Weber's cross-ice pass inside the blue line and drove a slap shot to the left of the net.
"He had a clear lane to shoot it right on the net. As soon as he shot it wide I knew that this was a set play," Biron said.
Gomez, who was positioned to the right of the net, gathered the rebound off the end boards on his backhand and moved the puck to his forehand before snapping a rising shot past Biron and into the top of the net.
"We know our boards here are really lively, but I'll be honest, I did not see Gomer," Picard said. "I just didn't want a shot to get blocked so I knew by shooting the puck pretty hard against the boards it would come back in front. There was a lot of traffic, and Gomer made a really nice play and showed some good hands on that goal."
Biron is 8-5 in 16 games, including a relief outing in Thursday's 3-2 loss to New Jersey. He stopped all six shots he faced after coming on in the second period to replace All-Star Lundqvist, who allowed three goals on 12 shots.
"Biron played very well," said Tortorella, who recently singled out Lundqvist's recent play as a key reason for New York's current skid. "I thought Biron played well, and Price played well, also."
Rangers captain Chris Drury didn't make the trip after having fluid drained from his left knee on Friday. There is no timetable for his return. ... Lundqvist has lost each of his last four starts against Montreal, including two this season. ... Price's career high for starts is 49 in the 2008-09 season, when he played in 52 games. ... Picard fought Sean Avery in the first and took an interference penalty midway through the second. He was a healthy scratch for 13 of Montreal's previous 15 games, including 10 in a row since his last game on Jan. 8.