Connor Hellebuyck turned away 35 shots with 28 of those coming in the first and third periods combined.
But the one he wants back is Joe Pavelski's overtime winner. The Sharks forward took a pass from Brent Burns on a 2-on-1 and snapped it past Hellebuyck on the glove side.
"It was a good shot. I'll give him that. But on the other hand I want to find a way to stop it," said Hellebuyck, who earned praise from his teammates for his play in the game.
"I could potentially stay on my feet, or get my glove up right away or get my glove out," Hellebuyck said. "That's just off the top of my head. I'd have to see exactly how it went."
For the third time on the home stand, the Jets opened the scoring.
Wheeler's wrist shot from the left wing off the rush went through the legs of Sharks defenceman Justin Braun and over the left shoulder of Martin Jones. The Jets captain's 11th of the campaign came 3:08 into the period.
But San Jose (31-16-7) found the equalizer on the power play just after the midway mark of the first period. Logan Couture's wrist shot beat a screened Hellebuyck with 9:06 left in the period. Seconds before, Josh Morrissey blocked a one-timer and had trouble getting to his feet. Shortly after the goal was scored, he went down the tunnel to the Jets dressing room.
"He's day-to-day. He may play in Montreal. We'll see how he comes back tomorrow," said Jets head coach Paul Maurice. "There is no major concern on it. We'll see how he's moving tomorrow."
A Tyler Myers pinch at the Sharks blue line kept the puck on side by mere inches, but it was enough to set up Winnipeg's second go-ahead goal. Brandon Tanev's feed in front then went off Myers' stick to Perreault, who beat Jones five-hole to give the Jets a 2-1 lead.