The Sharks, who began a four-game trip that continues at the Toronto Maple Leafs on Wednesday, have won seven straight games, all in regulation, at Montreal since a 2-0 loss March 21, 2015.
"It wasn't the most smooth game," San Jose forward Matt Nieto said. "But I think we just stuck to the process, and if we got hemmed in we just locked it down and got through that shift and didn't give up massive opportunities for them to score. And obviously Kaapo back there was a wall for us."
Nieto gave San Jose a 1-0 lead at 1:33 of the first period. He jammed in a loose puck in the crease after Allen got his left pad on Alexander Barabanov's wraparound attempt.
Montreal went 0-for-6 on the power play, including a 5-on-3 advantage for the first 55 seconds of the third.
"We did have a plan, we just didn't quite execute the plan and we just looked disorganized," Canadiens coach Martin St. Louis said of the two-man advantage.
The Sharks have allowed six power-play goals in 25 games and lead the NHL with a 91.2 percent success rate on the penalty kill.
"Killing them with the success rate we have, you know, you have a swagger to you when you kill penalties," San Jose coach David Quinn said. "So I thought we had good swagger tonight. We've had swagger for a while killing penalties."
Hertl made it 2-0 at 2:29 of the third when he redirected Kevin Labanc's pass past Allen stick side from the slot.
Couture increased the lead to 3-0 at 3:44. He shot between Allen's pads on a clean breakaway after taking Matt Benning's long pass up the middle.