Price made 29 saves and Montreal extended its winning streak to three games with a 3-0 victory against the Winnipeg Jets at Bell Centre.
Tomas Plekanec scored a shorthanded goal into an empty net with 36.7 seconds remaining.
"[Price] was spectacular again for us, as usual," Plekanec said. "It wasn't a perfect game for us. We had some problems executing our plays but at the end of the day we managed to score three goals."
Winnipeg forward Evander Kane had a shot at a wide-open net moments before Plekanec's goal, but Markov deflected it over the goal to preserve Price's 26th career shutout.
"That was big for me, personally. [Markov] never gave up on the play and found a way to get his stick on it," Price said.
"It was good to get one," Price said. "We needed the win, first and foremost, but it was just icing on the cake."
Ondrej Pavelec stopped 24 shots for the Jets, who had their eight-game point streak snapped, the longest since the team relocated to Winnipeg in 2011.
"We didn't get enough pucks to the net early, and I don't mean [early] in the game. I mean early in our chances, early in our decisions to get it to the net," Jets coach Paul Maurice said. "We passed off probably too much and then it got knocked down or blocked.”
The Jets fell one game short of matching the franchise record nine-game point streak set in 2005-06, when Atlanta went 6-0-3 from Dec. 9-28.
It was Winnipeg's first regulation loss since Oct. 24.
"It's been a while, so nobody's in a very good mood back there, which is good," Maurice said. "You don't like to get comfortable with that."
Montreal forward Jiri Sekac drove the right side on the play that led to Eller's goal at 2:21 of the second. Pavelec poked the puck off the Czech rookie's stick as he cut towards the goal, but it went right to Eller, who played it up with his right skate to put a backhand into an open net.
"We're putting a lot of passes together, but most of the time that's going to be the goals," Eller said. "It's going to be driving the net and rebounds. Jiri had a good drive to the net there, you know, created space for me, and I picked up the rebound. A lot of times it's as simple as that."
Galchenyuk reached around Winnipeg defenseman Zach Bogosian to score his fifth goal of the season on a shot that Pavelec got a piece of with his stick, but was unable to prevent from going into the net.
"I saw it kind of develop and [Kane] had some help on the play," Price said. "I didn't want to quite cheat too much to the middle but I gave him a little bit of extra room on the blocker side and kind of guessed it a little bit … anticipated, I guess, would be a better word … and I just got a pretty good piece of it, so I was lucky a little bit."
Winnipeg center Mark Scheifele fired a shot off the left post on a shorthanded breakaway at 15:56 after Canadiens defenseman P.K. Subban turned over the puck with an ill-advised drop pass at his own blue line.
"I'd like to get one on the inside of the post one of these days instead of the outside," Maurice said. "We had a few."
Subban, who played his 300th game, was stripped of the puck by Jets forward Michael Frolik in the second on another play that led to a Jets scoring chance but Price turned aside Bryan Little's shot from the right side.
"Every night, [Price] is just unreal," Montreal center Manny Malhotra said. "It gives a team a lot of confidence when you know your goalie can make those types of saves. Obviously we don't want to have to make him make those 10-bell saves every night, but knowing that he has the ability and he believes in himself every night that he can stop every puck, it makes us play a lot bigger."
Toby Enstrom played his 500th game for the Jets/Thrashers franchise. According to the Elias Sports Bureau, Enstrom is the 11th defenseman selected in the eighth round (239th by Atlanta in 2003) of the NHL Draft or later to play at least 500 games with one team.
Left wing Drayson Bowman drew into the lineup in place of Moen and played 6:06 in his Canadiens debut.
"First of all, we let go a good leader, a good person, a guy that never complained, was always there for his teammates, always accepting his role," Therrien said. "On the other hand, we're going to get a guy that, first of all, I know really well. A really good person, and he's a good leader as well.
"[Gonchar] likes to care of his own teammates, you just have to ask [Evgeni] Malkin. He took him under his belt when Malkin started in the League and he stayed with his family for about two, three years, so he's that type of person.
"I spoke to him [Tuesday]. He's excited about coming to play in Montreal and we'll go from there, but he's a guy who's going to bring us some depth with our defense."