Gorges scored 1:45 into overtime and the Canadiens edged the Phoenix Coyotes 3-2 on Thursday night.
"The puck was squeezed out to me and I thought I'd try and put it on net," Gorges said. "We knew it was going to be a battle. You have to work against this team."
Brian Gionta had a goal and an assist, and Travis Moen also scored for the Canadiens, who snapped a two-game losing streak.
Mikkel Boedker and Raffi Torres scored for the Coyotes, who lost for the second time in three games but have earned points in seven of eight.
"It's disappointing when you felt like we had a pretty good week and were feeling good about ourselves," Phoenix coach Dave Tippett said. "It's the desperation level that you need to win, and that desperation level led to a lot of one-on-one battles that we lost."
The Canadiens were playing without left wing Michael Cammalleri, who hurt his knee Tuesday against Edmonton.
"When you have guys out you have to have other guys chip in," Canadiens goalie Carey Price said. "It was nice to see Josh finally get rewarded."
Torres tied it with 14:50 left, taking advantage of a convenient bounce. Keith Yandle's initial rebound shot dropped into the crease, just to the left of Price's leg, and Torres flipped the puck into the open right side of the net to make it 2-2.
"We came out with a quick goal, but we didn't build on it," Torres said. "As a team, had we been more physical, we would have been able to take the game away more."
Boedker gave Phoenix a 1-0 lead at 5:43 of the first. Cal O'Reilly passed the puck from behind the net to Boedker on the doorstep in front of Price for an easy one-timed goal, his first since Oct. 13.
Gionta made it 1-1 at 3:28 of the second, stealing the puck off Boyd Gordon's stick behind the net and beating Mike Smith on a quick wraparound.
"Gionta got him from behind," Montreal coach Jacques Martin said. "It was a surprise to him. He lifted his stick, took the puck and scored."
Moen made it 2-1 with 2:14 left in the period, taking a pass from Gionta and scoring on a wrist shot from the left circle, just inside the hash marks.
The Canadiens are 12-2-4 against the Coyotes since the team moved to Phoenix from Winnipeg, and haven't lost to them since 1998. ... Montreal C Tomas Plekanec was shaken up early in the first when he was driven into the boards by Oliver Ekman-Larsson. He returned and earned the second assist on Moen's goal. ... Coyotes C Daymond Langkow left the team Thursday because of a death in his family. His return date hasn't been announced. ... Coyotes LW Radim Vrbata came back into the lineup after missing two games with an undisclosed lower body injury. ... Coyotes C Martin Hanzal played in his 300th NHL game.
Copyright by STATS LLC and The Associated Press
Arena: Gila River Arena Location: Glendale, Arizona
Referees: Tom Kowal, Wes McCauley Linesmen: Andy McElman, Dan Schachte
Attendance: 14,138 (82.6% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Mikkel Boedker (2)
Assists: Cal O'Reilly, Oliver Ekman-Larsson
Brian Gionta (4)
Travis Moen (5)
Assists: Brian Gionta, Tomas Plekanec
Raffi Torres (3)
Assists: Keith Yandle, Boyd Gordon