"We've got to be a desperate team," Winnipeg coach Rick Bowness said. "It's down to crunch time. We've just got to embrace that fight and embrace it together as a group and keep fighting. Fight with each other and put it all out there. That's all we can do."
Connor Hellebuyck made 27 saves for the Jets (41-31-3), who lead the Calgary Flames by two points for the second wild card from the West after the Flames won 2-1 against the Los Angeles Kings on Tuesday.
Winnipeg is just three points ahead of the Nashville Predators, who also won Tuesday, 2-1 at the Boston Bruins. Nashville has played two fewer games.
"It's a tough loss, for sure," Jets forward Mark Scheifele said. "We're in the thick of it, we're in the fire, and that's where things are molded."
Noah Gregor had a goal and an assist for the Sharks (20-39-15), who had lost nine in a row (0-6-3). Their previous win was a 3-2 overtime victory at Winnipeg on March 6.
"It's as solid of a win as we've had in a while, and we haven't had a win in a while," San Jose coach David Quinn said. "So, it was a good win. Obviously, 'Reims' played great, but they were opportunistic and it was a gutty performance in a lot of ways against a team that's fighting for a playoff spot."