A turnover at centre ice by Jason Spezza let Higgins go in alone and shovel a backhander one-handed under Ray Emery's pad 5:30 into the second period. It was Higgins' sixth career shorthanded goal.
Alex Kovalev scored in the second period and then three goals were scored in the final 1:16 of play - Andrei Markov into an empty net, Steve Begin, and Ottawa's Tom Preissing with nine seconds left.
The Canadiens (6-2-3) also got a solid game from goaltender David Aebischer as Ottawa outshot the home side 33-29.
Spezza scored his fifth of the season for Ottawa (5-6-0), which was coming off a 2-1 defeat in Boston.
The Senators dropped to 0-5 when the opposing team scores first.
The best chance of a tight-checking first period saw rookie Guillaume Latendresse ring a shot off the post. Officials checked the video replay to be certain it did not go in.
Late in the second frame, the Canadiens killed off a 56-second two-man Ottawa and less than a minute later, Alexander Perezhogin won a race for a puck in the Ottawa zone that allowed Sergei Samsonov to slip it across the crease for Kovalev's tap-in goal at 18:32.
Spezza flipped a puck into the slot and saw it go off Radek Bonk's stick into the top corner 6:19 into the third frame.
Higgins is now tied with Pittsburgh rookie Jordan Staal for the league lead in shorthanded goals with three.
The Canadiens play in Carolina on Thursday, while the Senators' next game is also against the Hurricanes on Saturday in Ottawa.
Notes - D Wade Redden missed a second straight game for Ottawa. Coach Bryan Murray wants his groin healed before he returns. . . F Peter Schaefer returned after missing four games, bumping Alexei Kaigorodov from the lineup. . . Montreal F Aaron Downey returned after missing five games with a concussion. F Garth Murray was scratched. . . The Canadiens drew their 70th consecutive regular-season sell-out crowd of 21,273.