The Sabres forward scored a tiebreaking power-play goal with 1:18 left when a dump-in caught Montreal goalie Carey Price out of the net, lifting Buffalo to a 2-1 victory over the Canadiens on Friday night.
"It must be a lucky day, so I'll take it," Moulson said. "I don't think I've had one off the stanchion before."
Tyler Ennis added a highlight-reel goal, and Jhonas Enroth made 30 saves as the Sabres rebounded from a home loss to Winnipeg on Wednesday.
"You never shoot it off the glass and hope it goes in the net," Sabres coach Ted Nolan said. "Once in a while, luck comes if you continue to do the right things."
It was the first win against Montreal in seven tries for the Sabres, who have won four of five after a 3-13-2 start.
P.A. Parenteau's third-period, power-play goal ended Montreal's scoring slump at 132 minutes, 36 seconds, but it wasn't enough for the Canadiens to avoid their second-straight loss.
Montreal coach Michel Therrien chalked it up to luck, too, just not the good kind.
"It's a bad break," he said of Moulson's game-winner. "There's nothing you can do against a bad break."
Buffalo's first goal was a stunner, and it came just 3:27 into the game.
Ennis skated through the right circle and around defenceman Alexei Emelin, but had to leap over Price in the crease. Falling with his back to the net, Ennis found the moving puck and flipped in a backhanded shot from the bottom of the left circle.
"I was thinking I was going pretty fast through the zone, and if I could just take it to the net I'd get a chance," Ennis said. "I got the puck back up on my stick and got lucky."
Tyson Strachan then sent a two-line pass to send Torrey Mitchell in on a breakaway, but the Sabres centre put a low shot wide of the left post.
Sabres right wing Drew Stafford was injured in the first period and didn't return. Nolan said Stafford was feeling better and would make the trip to Montreal for Saturday's game.
Enroth was challenged by a series of shots during a scrum in the crease about 8 minutes into the second period, but was saved by a whistle with the loose puck in between a series of skates at the edge of the crease.
"You need to get those breaks sometimes," Enroth said. "We need to keep building on those breaks and stay positive here."
Moulson nearly made it 2-0 midway through the second, but his shot went off the butt end of Price's goal stick and wide of the net.
The Canadiens had a chance on the power play just 55 seconds into third period, and they needed just 40 seconds to tie the game on a disputed goal.
Enroth had the puck under his skate for multiple seconds when Parenteau jammed it free and into the net. The play wasn't reviewable.
"He said that I needed to cover it 100 per cent," Enroth said. "If you ask me, I covered it with my foot. It shouldn't matter if you cover it with your glove or your foot, but playing against Montreal you're not going to get a lot of calls."
Montreal carried the period, and Enroth made several tough saves including a chest stop on Max Pacioretty with 15 minutes gone.
Emelin elbowed former teammate Gionta in the head at the 18:06, starting a mild skirmish and sending Buffalo to a late power play.
But Ennis' late dump-in took a wild bounce off the end boards to Moulson, who had skated hard into the slot. Moulson was left with an empty net to score the winning goal.
"That's the way hockey goes," Ennis said. "It doesn't matter how it goes in. As long as we get the win, we're happy.
"We drew it up on the bench exactly like that."
Price made 23 saves in the loss.
NOTES: The Sabres signed free agent forward Jean Dupuy of the Sault Ste. Marie Greyhounds to a three-year, entry-level contract. ... Montreal D Tom Gilbert was a healthy scratch.