"They're a good team, they're going to push back, we knew that," Burns said. "This time of year, you just have to forget about that one and move on to the next one, win or lose. You head [to Colorado] and got to get a win."
Kane gave the Sharks a 1-0 lead at 7:57 of the first period on a rebound in front off a shot by Burns.
After being outshot 11-6 in the first period, Colorado scored twice on 13 shots in the second.
"[The Sharks] are just really good. They're a really good team and they smothered us in the first period, and I thought we were really slow in the neutral zone, getting pucks up and tipping them in and forechecking," MacKinnon said. "We found some way to get some sustained pressure in the second and it paid off."
Landeskog tied it 1-1 at 8:21 on a redirection of a point shot by Barrie, who has six points (one goal, five assists) in his past three games.
"Barrie was involved right from the start and got better as the game went on," Avalanche coach Jared Bednar said. "Elite players find a way to generate offense even when the checking is tough, and that's what he did tonight."
Barrie scored his first goal of the playoffs to give the Avalanche a 2-1 lead at 16:31. Mikko Rantanen outraced Marc-Edouard Vlasic to the puck behind the Sharks net following Nikita Zadorov's clearing attempt and sent a pass to Landeskog in the slot for a one-timer. Jones made the initial save, but the rebound kicked out to Barrie, who scored with a slap shot from the top of the right circle.
San Jose anticipated an icing call on Zadorov's clear.
"Our players did and they let up, they relaxed for a minute and it obviously wasn't," Sharks coach Peter DeBoer said. "The lesson in that is don't assume anything in the playoffs. Play and make sure."