The Canadiens swept a two-game set with Vancouver and moved a point ahead of idle Toronto into first place in the North Division. Eight of Toffoli's nine goals this season have come against the Canucks.
Toffoli added an assist on Jeff Petry's empty-net goal.
Montreal forward Nick Suzuki had two assists. Weber had an assist on Toffoli's second goal, giving the 35-year-old defenseman seven points (two goals, five assists) in 10 games this season.
Toffoli and Anderson, as well as other newcomers including veteran forward Corey Perry, backup goaltender Jake Allen and defenseman Joel Edmundson, have fit well with a Canadiens team looking to build on an unexpected post-season run last year.
''We're having success because that was the goal from the get-go when we made those kinds of deals,'' Canadiens coach Claude Julien said. ''So far it's working out well.
''We're 10 games in so that's certainly encouraging, but as I often mention it's a long year and we've just got to keep plugging away.''
Antoine Roussel, Elias Pettersson and Tanner Pearson scored for the Canucks.
''I thought we played well tonight,'' Canucks coach Travis Green said. ''Played like a team that knew what it needed to do to win. It was a grinding game early, slowly got a few more chances, just came up short.''
Jake Allen made 36 saves for Montreal. Thatcher Demko stopped 28 shots for Vancouver.
Montreal, which kicked off the two-game series between the teams with a 6-2 win on Monday, improved to 4-0-1 against the Canucks, outscoring them them 28-15 over five games.
Weber's 1,000th game was acknowledged at a stop in play midway through the first period. Players from both teams tapped their sticks on the ice and Weber waved as crowd noise was piped into the empty Bell Centre.
''Maybe it's a little unfortunate that his family and friends couldn't go to the game with the situation going on, but I thought they did a tremendous job,'' Anderson said Weber's tribute.
''Not every day you get to play your 1,000th game and it was such a special night just to be a part of it, and seeing Webs being such a great leader and going through that.''
NOTES: The Canadiens will show a video tribute during Montreal's game Thursday against Ottawa as part of ceremony with Weber's family present. Additionally, a painting of Weber will be unveiled and he will be presented with a silver stick by Canadiens general manager Marc Bergevin. ... Weber has 220 goals and 357 assists over 1,000 games. ... Roussel returned to the Canucks' lineup after being held out as a healthy scratch on Monday.
Canucks: Play the first of three games in Toronto on Thursday.
Canadiens: Host the Ottawa Senators on Thursday.
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