The rookie is rewarding their faith with a stellar first season.
Varlamov also had his second assist of the season.
Colorado is having a bounce-back season after finishing at the bottom of the Western Conference last year.
The rebound started with earning the top pick in the draft, and the Avalanche opted for the speedy MacKinnon instead of homegrown defenseman Seth Jones.
The decision has paid off. MacKinnon has 20 goals and 40 points to lead all rookies in scoring.
"I've been feeling more comfortable. I think I was a little snake-bit at the beginning and could've score more than I did," said the 18-year-old MacKinnon, who had his first three-point game. "Thankfully things are clicking, I've developed chemistry with guys on the team."
The Avalanche were playing their final home game before going on a four-game East Coast road trip ahead of the Olympic break. They have won eight of 10 and are 35-14-5. It's their best start to a season since 2000-01 when they won the Stanley Cup.
Colorado continued its mastery over the Sabres. The Avalanche have won seven straight against Buffalo.
"We weren't ready to go from the get go," Buffalo coach Ted Nolan said. "We never laid a body on anyone. It was a very ugly game to watch."
The Avalanche jumped ahead early and didn't need to sweat out the end as they did against Minnesota on Thursday.
They scored three quick goals on Olympian Ryan Miller in the first. Barrie started the flurry with his seventh of the season at 7:37, and McGinn and Landeskog had goals 58 seconds apart later in the period.
MacKinnon feathered a pass through the defense to Landeskog, who tapped it into the empty net.
"He's a special player," Avalanche coach Patrick Roy said of MacKinnon. "The third goal, the speed he put on on the ice was magic. Landy ended up with an open net. It was such a nice play. I see huge improvement in his game."
Cliche made it 4-0 early in the second.
"I just said, `finally," Cliche said. "So much weight off my shoulder. I know maybe I'm not supposed to score, but when you score one like that it feels unbelievable, especially in a 7-1 win like this."
Were his teammates happy to see him get his first goal? Indeed.
After all, he's been doing the dirty work for Colorado all season.
"We wanted him to score that for so long and he's had so many chances lately, it was great to see him score that one," Landeskog said. "The whole bench erupted. He's such an awesome team guy, he doesn't complain, he goes out there and does his job. Tonight he finally got rewarded for his hard work."
Miller is headed to his third Olympics for Team USA, but he didn't look sharp against Colorado. He allowed three goals on his first 11 shots and finished with 22 saves. He was pulled in favor of Jhonas Enroth to start the third period.
Enroth had 10 saves.
"It's obviously a hard game for us. A very tough game for us," Miller said. "We have to come to compete from the start. That's where we lost the game."
Miller didn't receive much offensive support from his teammates, who had just 10 shots on goal midway through the second. The Sabres finally broke through when Matt D'Agostini scored on the power play at 11:45 of the second.
MacKinnon answered on a power play later in the period to make it 5-1.
Landeskog and McGinn scored 2:31 apart in the third to make it 7-1.
Colorado D Erik Johnson had three assists. ... Avalanche C Paul Stastny (ankle) and RW Alex Tanguay (knee) were scratched. ... Buffalo D Christian Ehrhoff was back in the lineup after missing Thursday's game due to an illness. ... Colorado RW P.A. Parenteau returned to action after being a healthy scratch for two games. He assisted on Landeskog's goal.