Landeskog brought the Avalanche within 4-3 at 8:59 of the third, shooting glove side, and Kadri tied the game with a shot from a sharp angle for his first goal in 20 games.
"It felt good, for sure," Kadri said. "The time of the game, obviously we needed a goal. The guys kept encouraging me to shoot it and finally one went in."
Burakovsky won it with a shot that trickled in under Jones' glove.
"Mikko changed, so I came on the ice and Cale [Makar] gave me the puck," Burakovsky said. "I'm not sure what happened, but I found a lot of room in the middle of the ice. I don't know if they were changing or what they were doing, but I found some ice and I felt like [Sharks defenseman Brent] Burns was standing pretty low, so I shot. Definitely nice to see it go in.
"It's a really big one. We want to be in first place in the League and I think this was a must-win for us. We talked about it, we needed to come out harder, to leave everything we have on the ice. We just had to find a way to get this done, and we did, so great job by everyone."
Kane gave the Sharks a 1-0 lead at 3:20 of the first period, skating down the slot after a turnover by Valeri Nichushkin.
Rantanen tied 1-1 at 5:38, converting the rebound of MacKinnon's shot after Landeskog won a face-off in the right circle.