Carey Price made 28 saves for Montreal, which lost to Boston for the third straight time and fell to 3-8 since Randy Cunneyworth took over as coach.
Yannick Weber scored for the Canadiens.
Montreal won the first two matchups against the defending Stanley Cup champions, winning home-and-home games at the end of October. But since then the Bruins have won 25 of 30 games.
The game lacked the usual intensity of a matchup between the Original Six rivals — to the point where the crowd decided to entertain itself in the third period with derogatory chants about Tim Tebow, the Denver Broncos quarterback who will face the New England Patriots on Saturday.
But just a few minutes later, P.K. Subban elbowed David Krejci near the benches and Bruins defenseman Andrew Ference quickly came over to intervene. Ference was given four minutes and Subban two, resulting in Montreal's second power play of the game.
Twenty-nine seconds in, Weber put a screen shot from the right point past Thomas to make it 2-1. That was the first goal in 113 minutes for Montreal, which was shut out 3-0 by the St. Louis Blues on Tuesday.
The Bruins took the lead on a fluke goal just 83 seconds in, when Johnny Boychuk sent the puck around the boards and it took an odd bounce. Carey had gone behind the goal to play the puck, but it rolled right in front of the crease and Caron, who was recalled from Providence earlier in the day, put it into the empty net.
That's the way it stayed until 3:43 into the third, when Krejci dug the puck out of the boards and sent it behind the net to Nathan Horton. He passed it to Lucic in the slot, with a deflection of Tomas Plekanec's skate that forced the Bruins forward to switch to his backhand before quickly swiping it past Price into the net.
That extended Krejci's point streak to a career high-tying 10 games — the longest point streak in the NHL this season.
Notes: Bruins D Zdeno Chara and F Tyler Seguin will join Thomas and the team's coaching staff at the Jan. 29 All-Star game in Ottawa. ... Caron, a first-round pick in 2009, has skated in 14 games for the Bruins and 12 for the Providence Bruins of the AHL this season. ... Canadiens C Petteri Nokelainen returned to the lineup after missing two straight games. ... Montreal was again without captain Brian Gionta who left Tuesday's game against St. Louis in the third period and underwent bicep surgery on Wednesday. ... Bruins F Marc Savard will purchase a luxury suite for each remaining home game for pediatric patients at Children's Hospital Boston, with a focus on children suffering from the effects of head trauma. Savard was expected to attend the game, but his flight was canceled due to the weather.