Kaapo Kahkonen made 36 saves, and Alexander Barabanov scored for San Jose (17-28-11).
"Our goalie was outstanding tonight. I thought it was his best game of the year," Sharks coach David Quinn said. "I'm just really disappointed we couldn't finish it off in the last 17 seconds."
Vegas leads the NHL with nine third-period comeback wins this season.
"We have a confidence in ourselves going into the third," Golden Knights forward Jack Eichel said. "If we're down a goal or if the game's tied, we feel comfortable to find ways to win. You saw that tonight. You've seen in the past a few times. I would love it if we were going into the third with a lead more often and not chasing games, but it's good to see we're finding ways to win and come from behind."
Barabanov gave San Jose a 1-0 lead at 17:04 of the second period, putting in a rebound off of a Marc-Edouard Vlasic shot from the left point. He has a point in six of his past seven games (four goals, two assists).
"He's a really smart player," Quinn said of Barbanov. "He's strong on his skates for a small guy (5-foot-10, 195 pounds). He makes real good decisions with the puck. … He generates a lot of offense. When the puck's on his stick, good things usually happen."
Cotter tied it 1-1 at 6:22 of the third period. He kept the puck on a 2-on-1 with Jonathan Marchessault, shooting it past Kahkonen from the right circle. He had an opportunity on a 2-on-1 breakaway at 3:33 of the third, but Kahkonen managed to get to his near post to stop the shot.
"He has a breakaway earlier by getting available. He made a nice move. The guy made a save. [Next] time, he decided to rip it, it just worked out for us," Cassidy said. "It was a big goal. He's more of the guy who will shoot it. It shows in his numbers. You need some of those guys. I'm glad he shot it tonight. He does have a good shot. He has the ability to beat the goaltender."