Max Pacioretty had two goals, Weise scored on a penalty shot, and the Montreal Canadiens beat the Bruins 5-1 on Thursday night for their fourth straight win.
Weise, a checking forward, scored his first goal of the season and added an assists.
"I think as a team that was our best outing," Weise said. "Just a complete game.
"Our goaltender didn't have to stand on his head tonight. He made some great saves, but our offense was there. I just felt we had a complete effort from everybody."
It was Weise's first meeting with the Bruins since Montreal's seven-game win in the playoffs last spring. He was scratched for Montreal's 6-4 win over Boston on Oct. 16. But other than a first-period scuffle with Gregory Campbell, Weise stuck to hockey and was named first star of the game.
"Our whole team gets up for Boston," he said. "It's a playoff atmosphere every night. The crowd was into it from the start.
Lars Eller and Jiri Sekac also scored for Montreal (12-4-1), which saw Sergei Gonchar's debut after he was acquired Tuesday in a trade with Dallas.
Dougie Hamilton scored a power-play goal for Boston (10-8-0), which lost badly for a second game in a row after a 6-1 setback in Toronto on Wednesday night. The Bruins were playing a third game in four nights.
The Bruins had won five in a row before crossing into Canada.
"For the most part, teams that have to go through these kind of situations normally grow from it, and that's what we hope we can do here," coach Claude Julien said. "We need to get better, we know that."
With Tuukka Rask pulled after allowing four goals on 16 shots in Toronto, Niklas Svedberg got the start for Boston and faced 34 shots. Carey Price made 21 saves for Montreal.
The Bruins came out of the first period with a 1-0 lead on Hamilton's goal from Patrice Bergeron's faceoff win only four seconds into a man advantage at 16:04.
Fatigue started to show in the second as Boston took three straight penalties.
The first was a penalty shot at 2:31, as Dennis Seidenberg lost the puck and then tripped Weise. The Canadiens fourth-liner beat Svedberg between the pads.
Confusion behind the Boston net let Brendan Gallagher poke a pass in front for Eller, who scored his third goal in three games. Pacioretty added another less than two minutes later, at 14:57, on a one-timer off a feed from Weise.
Pacioretty was at the crease to get a stick on a David Desharnais pass that deflected off Hamilton's skate 5:09 into the third.
Sekac took a Nathan Beaulieu feed and went in alone on the left side to score on a wrist shot on a power play at 14:06. The goal ended an 0-for-27 run without a power-play goal for Montreal. It was only the Canadiens' fourth this season, and three have come against Boston.
"This is the game we've been searching for a while," said Pacioretty. "We've been relying too much on Carey Price the last couple of games. It feels really good to put some in for him and take some pressure off him for once."
Gonchar had the Montreal power play looking livelier all night, although he wasn't involved in the goal.
Notes: With Gonchar in, Montreal dressed seven defensemen, with Beaulieu taking some shifts on left wing on the fourth line. Gonchar played on the first power-play unit with Andrei Markov. ... The Bruins were missing injured captain Zdeno Chara and first-line center David Krejci. ... Boston's Matt Fraser was knocked wobbly from a punch by Beaulieu during a second-period fight, but he was back for the third. ... The teams meet again Nov. 22 in Boston.