Brent Burns and Joe Pavelski each had a goal and an assist, and Justin Braun scored for San Jose (13-10-5), which was outscored 20-7 in its previous four games (0-3-1) of a five-game road trip.
"That's a way better game, how we played," said Jones, who made 22 saves in the third period. "Despite the shots, it's the 2-on-1s and the odd-man rushes that have been hurting us, so we thought we did a great job tonight."
WATCH: [All Sharks vs. Canadiens highlights]
The Sharks held a team meeting with general manager Doug Wilson earlier in the day.
"The tone was, 'We can figure this out, we have the team to win games in this League,'" San Jose forward Logan Couture said. "It takes a full buy-in from everyone to do things right and I think tonight is a step in that direction. I thought we did a lot of the little things well tonight.
"We got in shooting lanes, we played hard, you know, we were hard on the walls. I think we can still do a better job at getting pucks out in the third when they pinched down a bunch of times, but we'll take the win."
Jeff Petry scored for Montreal (12-10-5), which is 1-4-2 in its past seven games. Carey Price made 26 saves.
"We knew they were going to be hungry and I think they were the better team in the first period," Petry said. "And as the game went on, I think we got better, but that's something that we need to do from the start. You know, I think we've won one of our last [seven] so there's no reason we shouldn't be desperate as well to get points and to move up in the standings."
Braun gave San Jose a 1-0 lead with his first goal of the season at 2:55 of the first period. After intercepting a pass from Petry in the neutral zone, he skated in over the blue line and scored on a slap shot that beat Price five-hole.
"It was my fault," Petry said. "I kind of hesitated and [Braun] read that I was going to make the pass. And I took a split second and he read it and just stepped in front. When I look there, I think the safer play was just to chip it in the neutral zone and play it a little safer there."