The winning streak is the third longest in Devils history, trailing 13 games in 2000-01 and 11 in 2005-06.
"We knew they wanted to attack from our mistakes," New Jersey defenseman Jonas Siegenthaler said. "We just tried to limit our mistakes and have good gaps against them and give them nothing, be close to them, don't even give them a shot, and I think we were pretty good tonight."
Jake Allen made 34 saves, and Evgenii Dadonov scored his first goal for Montreal (8-7-1), which ended a season-high three-game winning streak.
"We knew they were playing well," Canadiens captain Nick Suzuki said. "They're a fast team, they're up and down the ice real quick, and I think we couldn't really find solutions early. We were on our heels a lot, playing in our own zone, and it's not a good recipe for us."
Hughes gave New Jersey a 1-0 lead at 3:57 of the second period, scoring from the left face-off circle on a power-play for his 50th NHL goal.
"[Hughes] really stayed with it the whole game and he played really good with the puck," Bratt said. "And he was creating a lot, especially on the power play there, he was willing to shoot. And he was a big threat for us all game and he really shows what kind of player he is when he gets the chance to make something happen."
Hamilton made it 2-0 at 6:06, snapping a wrist shot under the crossbar on a 2-on-1 after stripping the puck in the neutral zone.