Kevin Porter and Stefan Elliott also scored for Colorado, which went 8-1 at home in December. But Colorado's celebration was tempered because of a right knee injury sustained by center Matt Duchene early in the first period.
Duchene got hurt as his right skate got caught in a rut in the ice as he tried to deliver a check. He skated to the bench and went immediately to the locker room. Duchene wore a brace on the right knee after the game.
"I just saw it on video, it looked like he tweaked it," Colorado coach Joe Sacco said. "He'll be re-evaluated in the morning."
The 20-year-old Duchene leads the Avalanche with 12 goals and is second on the team with 24 points.
"He's without a doubt one of the best players in the league," Landeskog said. "It's definitely a big blow to us, but at the same time we have a good team in here."
Landeskog netted the winning goal after Chuck Kobasew did the dirty work. Kobasew battled Adrian Aucoin along the boards before floating a pass to Landeskog, who beat LaBarbera between the pads with 10:50 remaining.
"Chucky did a great job of staying with that puck," Landeskog said. "He kind of fed me, and I got some room there, I tried to get it low on net and was able to sneak it in five-hole."
LaBarbera went off for an extra skater with 50 seconds left, but the Coyotes couldn't get the tying goal.
Boedker's second goal with 2:21 left in the second period got Phoenix even at 2. The game then got chippy when Lauri Korpikoski ran into Varlamov, irking the goalie's teammates.
With 1:38 left in the period, Raffi Torres hit Colorado defenseman Jan Hejda in the head with a check while Hejda was vulnerable. Hejda was down on the ice for a few minutes before skating off with help from the Avalanche's trainer. Heda returned to the game in the third period.
"I thought the referees, obviously, they had a tough night," Sacco said. "They missed that hit there, but we're fortunate Jan was able to come back."
"It's frustrating. We've played a lot of tight hockey games and we can't find a way to get on top of them," Phoenix coach Dave Tippett said. "That's seven one-goal games in a row, and we've only won two of them."
Porter used good timing to put the Avalanche ahead 1-0. After serving a penalty for too many men on the ice, Porter jumped into an odd-man rush and redirected Paul Stastny's centering pass past LaBarbera 7:44 into the game for his third goal of the season.
Boedker tied it 1-1 when he wristed a rebound over Varlamov's right shoulder at 12:31. Elliott gave Colorado a 2-1 lead when he skated into the Phoenix zone and beat LaBarbera with a shot from the slot with 4:32 left in the first.
"Just trying to shoot the puck," Boedker said. "That's something I've got to do more of -- shoot the puck and take it to the net. It's not very fun after a loss."
Colorado leads the NHL with 14 one-goal victories. ... The Avalanche's eight home wins in a month tied a franchise record set in March 2008. ... Colorado has allowed three power-play goals in eight games. The Avalanche have killed 27 of 30 penalties in that stretch. ... The game marked the sixth set of back-to-back contests for the Coyotes. They are 4-2 in the second game. ... Kobasew returned to the lineup after missing eight games with a head injury.