"It could have been a lot easier, to be honest," said Bernier, who has won seven in a row and made 24 saves when the Avalanche killed all seven Sharks power plays. "We didn't stick to our game plan, we tried to be fancy a little bit when we got the lead."
WATCH: [All Sharks vs. Avalanche highlights]
Carl Soderberg, Mikko Rantanen and Matt Nieto also scored for the Avalanche (25-16-3), who have gone 13-3-1 in their past 17 games.
After seeing their lead slip from 4-0 to 4-3, Nieto tipped Blake Comeau's pass behind goalie Martin Jones (17 saves) with 3:14 remaining in the third period for a 5-3 lead. It was his ninth goal.
"It was nice to get that insurance goal," Nieto said. "I just drove to the net, he threw it there and it was kind of a lucky tip. It wasn't an easy game, but we found a way."
Timo Meier, Marc-Edouard Vlasic and Joe Thornton scored for the Sharks (24-14-6), whose winning streak ended at three.
"We had probably three, four Grade-A chances to tie it up," Sharks coach Peter DeBoer said. "You have to give their goalie some credit. He made some big saves in the third. I don't think it was too deep of a hole. We had a legit chance to tie it.