Weber scored against his former team and Subban had two assists in a game in which Smith's team-leading 13th and 14th goals of the season were the difference.
''He had a super strong game,'' coach Peter Laviolette said of Smith. ''He was physical, he was fast, he was competitive on pucks. And obviously he chipped in on offense as well.''
The Predators were playing their second game in as many nights, coming off a 4-3 overtime loss to the Detroit Red Wings on Friday. But Nashville came out with speed and the Canadiens couldn't match it.
Smith extended his personal point streak to five games when he put Subban's rebound past Carey Price at 10:44 of the first period to give the Predators a 1-0 lead. Smith has scored in three straight games.
The Predators outshot Montreal 16-11 in the first period as the Canadiens lost for the first time in three games.
''Tough first period really set us behind,'' said Weber, who scored his second career goal against Nashville. ''Tough team to come back against. They played last night and they came out with a better effort to start the game. They caught us sleeping.''
Weber got one back for the Canadiens at 12:47 of the second period when he threw a bouncing puck on net.
Smith answered 18 seconds later on a wraparound. Subban's assist on the goal was his 300th in the NHL.
''It was simple,'' Smith said of his second goal. ''It was a hard forecheck. We got it up. Subby just found a hole to get it in. And you never know what could happen.''
The Canadiens felt Smith prevented Price from making the save and challenged for goalie interference, but the call on the ice stood.
''I haven't seen the replay of it so I can't make a fair assessment of it,'' said Price, who made 28 saves. ''But it was explained to me that I made contact outside the crease. It's a moot point because it was their third goal and we obviously only scored one.''
Viktor Arvidsson scored into an empty net with 45 seconds left for Nashville.
''That's what you have to do on the road. You can't give teams breathing space,'' Subban said. ''For me to just come in and get two points, for our team to get two points on the road, that's big for us. We haven't had much consistency on our team for the past 15 or 20 games, so it's a big win for us.''
NOTES: The Predators play four more games on their current season-high six-game trip. ... Weber and Subban faced off for the first time on Mar. 2, 2017, when Montreal won 2-1 at Bell Centre. . This was the fifth game between Montreal and Nashville since the trade in the summer of 2016.
Predators: At Toronto on Monday.
Canadiens: Host Minnesota on Monday.
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