The Bruins increased their lead over second-place Montreal to five points in the Northeast Division.
Tim Thomas recorded the shutout, his eighth of the season and 25th of his career, by making 24 saves.
Johnny Boychuk opened the scoring 61 seconds into the game, and Campbell and Horton followed with first-period goals.
Horton, Adam McQuaid, Tomas Kaberle and Campbell scored in the third period -- Horton boosting his total for the season to 22.
Carey Price allowed five goals on 33 shots before being removed in favor of Alex Auld.
This was the first meeting between the teams since Boston defenseman Zdeno Chara delivered a controversial hit on Montreal's Max Pacioretty. Pacioretty was slammed into the side of a pane of glass between the benches, suffering a severe concussion and a fracture of the fourth cervical vertebra.