However, by 13:01 of the first period at MTS Centre, the Sharks trailed 3-0 and starting goaltender Antti Niemi was on the bench in an eventual 5-2 loss.
"The start was not what we needed in a building that just seems to build with energy," San Jose coach Todd McLellan said.
The win began a three-game homestand for the Jets (35-23-12) and moved them one point ahead of the Calgary Flames for the second wild card into the Stanley Cup Playoffs from the Western Conference.
San Jose (34-28-8) is six points behind Winnipeg, with nine of the Sharks' final 12 games against teams below the playoff line.
"It's a little setback, but it's far from over," Sharks defenseman Marc-Edouard Vlasic said.
"[Scheifele and Stafford] are buzzing right now," Wheeler said. "When [Scheifele] is skating like he is right now, he's great to play with. [Stafford] is just so strong on the puck. He makes such smart, simple plays; I think he makes a good complement for the two of us."
Jets goaltender Ondrej Pavelec started for the second consecutive game, the first time since Nov. 20-23, and made 38 saves.
"We got some really good goaltending," Jets coach Paul Maurice said. "He was just aggressive trying to find pucks. He was fighting."
Lowry scored 1:10 into the game when he muscled past San Jose defenseman Brent Burns in the left corner and banked a shot off the back of Niemi's right leg from behind the goal line.
San Jose defenseman Justin Braun's slashing penalty helped create Winnipeg's second goal. Scheifele took Toby Enstrom's cross-ice pass to the left circle and beat Niemi over the left shoulder at 9:39.
The Jets took a 3-0 lead 3:22 after Scheifele's goal. With Sharks forward Melker Karlsson off for high-sticking, Ladd tipped a point shot by defenseman Jacob Trouba past Niemi at 13:01 for his 24th goal.
Pavelski's goal off a long rebound from Pavelec 1:06 into the second period made it 3-1. Pavelski, who had one goal in his previous 12 games, made it 5-2 with 2:25 left in the third.
"Every game right now, if you don't win it, it's a setback, bottom line," Pavelski said. "Nobody in here can hang their heads right now. We've got to get ready for the next game."
Winnipeg led 4-1 7:05 into the second period when Wheeler jabbed a loose puck between Stalock's pads for his 21st goal. Wheeler made it 5-1 with 10:48 left in the game when he batted a puck past Stalock.
Stafford, since coming to the Jets in a trade with the Buffalo Sabres on Feb. 11, has five goals and five assists in 14 games. Scheifele has four goals and six assists in his past 10 games, and Wheeler has a five-game point streak (five goals, four assists).
"I'm just trying to ride this wave as much as I can playing with guys like [Wheeler] and Scheifele," said Stafford, who is a right-handed shooter playing on his off wing. "I feel as though we have some great chemistry."
Scheifele said, "I think we're just getting more comfortable playing with each other. I think we all just want to go out and make plays. We all want to play a hard game, we want to be fast, we want to take an opportunity when we get it."
Jets center Bryan Little missed his fifth consecutive game because of an upper-body injury. His absence placed more burden on Scheifele, who is in his second full NHL season, and Lowry, a 21-year-old rookie.
Scheifele and Lowry took 35 of the 58 faceoffs; Lowry had a Jets-high seven hits.
"I think every line is clicking," Scheifele said. "Every line is getting its chances, every line is creating offensive pressure, and that's what we want. We want a well-balanced attack."
"I don't care what happened before," Pavelec said. "Now is now. My job is to be ready whenever I have a chance to play, so that's my job."
San Jose plays at the Toronto Maple Leafs on Thursday. McLellan reiterated his message from the morning skate that the Sharks will need to bounce back quickly from adversity.
"We're moving on," McLellan said. "We've got to go to Toronto. By the time we [get on] the plane, we should be recharging our batteries and getting ready to play in Toronto.
"Now we get on the plane, we eat, we review the game, we have a good skate [Wednesday], we practice and away we go. There is nothing else we can do. We could sit in the corner and cry if we wanted to, but that's not going to help us one bit.
"If something negative happens, we've got to park it and move on. We have no other options."
The Jets host the St. Louis Blues on Thursday. With 82 points, Winnipeg is trying to catch the Minnesota Wild (85) for the first wild card while attempting to fend off Calgary (81), the Los Angeles Kings (81) and San Jose (76).
Winnipeg could have defenseman Dustin Byfuglien back against St. Louis. He participated in the morning skate Tuesday but missed his fifth game because of an upper-body injury.
"[Byfuglien] was ready to go, and he got through the morning skate," Maurice said. "But sometimes you have to pull a guy back a little bit, and I just didn't think it was the right time for him to come in.
"We want to be sure with [Byfuglien] that when he comes back in, he doesn't go back out again."