"We found a way to win," San Jose coach Peter DeBoer said. "We were a little fragile, but at the same time, I didn't think we gave them a whole lot. It seems like right now the chances we give end up in the net. I think there's a lot more good than bad, but we still have some work to do."
Nick Schmaltz, Brad Richardson and Richard Panik scored for the Coyotes (13-13-2), who have lost six of seven at home (1-5-1). Adin Hill made 28 saves.
"Played hard. [Down] 3-0 to that team, we come back, there's four of five minutes left in a tie game, we're right there," Arizona coach Rick Tocchet said. "I'm proud of the guys. The guys worked hard."
The Sharks played the second half of a back-to-back after losing 3-2 at the Dallas Stars on Friday.
"Back-to-back games, a tough loss to Dallas, a team we should beat, and we got the job done," Kane said. "It's nothing to hang our heads about, it's nothing to celebrate about, we won the next game."