Wheeler scored his team-leading 25th goal, had two assists and delivered a team-high five hits as the Jets stunned the Sharks 4-3 and delivered a huge blow to San Jose's hopes of winning the Pacific Division.
Tobias Enstrom scored the game-winner on a power play with 3:36 left in the third period, with Wheeler earning the primary assist. Wheeler got the puck below the goal line and sent a sharp-angled pass to Enstrom, who ripped the game-winner past Sharks goalie Antti Niemi from the left circle.
"He just keeps getting stronger and more powerful -- power play, penalty kill, 5-on-5, finishing checks, he's just been fantastic for us," Jets coach Paul Maurice said of Wheeler.
Winnipeg is nine points behind the Phoenix Coyotes, who own the second wild-card spot in the Western Conference.
"You check, but we're not thinking about it before the game," Ladd said of the playoff race. "We just wanted to come in here and have a good effort and give ourselves a chance to win, and I thought we did that."
Dan Boyle, Brent Burns and Logan Couture scored for the Sharks (47-19-9), who remain two points ahead of the Anaheim Ducks in the Pacific Division. But Anaheim has played three fewer games, and the Sharks wasted a chance to gain valuable points.
"We can't give away points," Sharks forward Joe Pavelski said. "We've given away a few too many lately. [The Ducks have] the games in hand. If they do their job, they'll be there, but there's still quite a bit of hockey left."
Niemi stopped 27 of 31 shots.
The Sharks and Jets entered the third period tied 3-3 after two penalty-filled periods. Each team scored two power-play goals in the game.
Winnipeg went on the first power play of the third at 14:17 when San Jose defenseman Brad Stuart went to the penalty box for holding Michael Frolik. San Jose killed off all but 11 seconds of that penalty when Couture flipped the puck over the glass and went to the box for delay of game.
"It's a very easy call," Couture said. "The puck goes out of play, it didn't hit the glass. I tried to backhand it down, and it kind of flipped up on me at the last second. Just unlucky. I'm not a big fan of that rule, never have been, but it's there and it cost us tonight."
The Jets quickly made San Jose pay, as Enstrom scored his ninth goal at 16:24. The goal came 27 seconds after Couture went to the penalty box.
Coming into the game, the Jets had defeated the Sharks 5-4 in a shootout at home and suffered a 1-0 loss at San Jose.
"I think we learned that we match up well against them," Wheeler said. "I think that gives you confidence going into a game. If it's a team that you don't really have a great matchup against sometimes, it can be a tough night, but for whatever reason we match up decent against these guys. They've all been one-goal games, and we've come out on the right side (twice)."
Boyle gave the Sharks a 1-0 lead 1:57 into the first period when he ended a 29-game drought with his ninth goal. Sharks center James Sheppard sent the puck from above the right circle to the slot, Marty Havlat redirected it toward the net, and Boyle tapped it in past Montoya.
"It's been a long time," Boyle said. "It was nice for a couple minutes, but obviously losing the game puts an end to that pretty quickly. It was nice to help put one in."
Ladd answered 36 seconds later with his 22nd goal. Racing along the right boards, Frolik sent a pass ahead to Ladd, who got behind San Jose's defensemen and tried to jam the puck past Niemi. Niemi stopped that effort, but he couldn't cover the rebound, and Ladd lifted it over his pads and into the net.
"You go back and think of the number of games ... where he's answered back right after the other team scored," Maurice said of Ladd. "That was big in this building because it can get real loud on you if they start getting chances. They really can run at you. It was big because it settled the game down, settled the bench down."
Ladd, who missed the Jets' game Monday against the Dallas Stars to be with his wife and newborn daughter, is tied with Bryan Little for second on the team in goals.
The Sharks regained the lead at 14:27 of the first period on the power play when Burns scored his career-high 21st goal. Pavelski hit Burns in the low slot with a pass from the right circle, and Burns lifted a backhand shot over Montoya's pads.
The Jets opened the second period with back-to-back goals by Wheeler and Byfuglien to take a 3-2 lead.
Wheeler scored his team-high 25th goal at 1:55, sending a sharp-angled shot from the right circle that somehow made it through Niemi's pads and over the goal line.
Then at 9:32 of the second, Byfuglien scored on the power play with Joe Thornton in the box for tripping Wheeler. Byfuglien took a cross-ice pass from Wheeler in the left circle and one-timed a laser past Niemi for his 20th goal on his 29th birthday.
"He's been dominant this last month or so with his speed and his confidence with the puck now," Ladd said of Wheeler. "I know firsthand playing with him, he's a guy that if you get open, he'll find a way to get you the puck. With his speed he creates so much space for himself. He gives himself time to make those plays. He's been great for us."
The Sharks tied the game at 3-3 at 11:23 of the period on Couture's power-play goal. Couture returned to the lineup and centered the second line after missing one game with an injured foot sustained blocking a shot Monday against the Calgary Flames. He paid a physical price for his 20th goal.
Sheppard blasted a shot that banked off Couture's thumb and into the net from just left of the crease.
Thornton became the 100th player in NHL history to appear in 1,200 regular-season games, but the Sharks played a forgettable one against the Jets, who had lost back-to-back games and have gone 5-6-3 since the NHL's break for the 2014 Sochi Olympics.
"You want to be consistent no matter who you play, but yeah, we've let some teams that are not as good in the standings beat us and take points away, for whatever reason I'm not sure," Thornton said. "We've got a game Saturday (against the Colorado Avalanche) that's important and just get our mindset back to we've got to win every game here on out and we'll be OK."