Wheeler, who also had an assist, has overcome early scoring troubles with three goals in the last three games to increase his season total to five. The 6-foot-5 winger has also been one of the Jets' best set-up guys with 19 assists as linemates Evander Kane and Bryan Little had been providing much of the offensive punch.
"I've been telling the guys to give me the puck once in a while and maybe I'll put it in," he said. "It's a team sport and our line has been putting the puck in the net. You want to ride the momentum ... you never want to be too picky, if you aren't the guy scoring. If they slow down a bit, maybe I can pick it up for a little bit."
Carey Price made 30 saves for the Canadiens, who lost their fifth straight.
Wheeler's first goal game on a pretty cross-ice pass from defenseman Dustin Byfuglien just three minutes into the game on the power play, and his second was a solo effort, racing down the right side and beating Price.
"The first [goal] was great," Wheeler said. "Byfuglien made a hell of a play. And the second one felt really good to just pick a corner finally."
Jets coach Claude Noel said Wheeler is tough to defend when he's moving his legs.
"When he skates and has the puck, he's a real factor," Noel said. "He's playing with more bite... when he plays like that, he's a hard guy to handle."
Montreal still hasn't won since interim head coach Randy Cunneyworth replaced the fired Jacques Martin last week.
The move to promote Cunneyworth, who played with the old Winnipeg Jets for a very short time during the 1989-90 season, has been controversial in Quebec because he doesn't speak French. It's been decades since the Canadiens have had a non-French speaking head coach.
"We realize what's going on to some degree," Cunneyworth said. "[The Jets] worked hard and we have to work a little bit harder. It comes down to battling and competing and we didn't have that compete tonight.
"You have to keep on trying and that's the bottom line. It comes down to competing, being physical and having some resolve in our play. I think it's about sticking together at this time. We are trying to figure out the pieces of the puzzle and everybody has to come together."
Pavelec wasn't tested much in the first and third period, but made 16 saves in the second as Montreal pressed with four power-play opportunities.
"All I want is the win ... two points," said Pavelec, who also had an assist on Wheeler's second goal. "I'm not going to lie, it's nice to have a shutout, but we got the two points.
"We played great defensively, blocked a lot of shots, I saw a lot of the shots, and all four lines did a great job."
Looking for a quick start against the slumping Canadiens, the Jets struck early with a power-play goal as Wheeler took a cross-ice pass from Dustin Byfuglien and scored 3:18 into the game with Montreal's Hal Gill serving a double-minor for high-sticking.
Despite allowing the two goals in the first period, Price was outstanding as the Jets outshot the Canadiens 13-6 over the first 20 minutes.
However, he gave up Wheeler's second goal of the game 39 seconds into the second period on a shot from the right faceoff dot that the goalie likely should have blocked.
Neither team mustered much offense in the third period, with Montreal looking tired and the Jets content to just chip the puck deep. Stapleton closed the scoring with 2:24 to go.