Senators goaltender Ray Emery stopped 27 shots to pick up his 23rd win of the season, matching his victory total from all of last year.
A sold-out Scotiabank Place crowd of 19,915 watched the Senators, who had lost 3-2 to the Sabres a night earlier at Buffalo, take an early lead on Montreal from which the Canadiens never recovered.
Anton Volchenkov added two assists for the Senators.
Guillaume Latendresse had the lone goal on a second-period penalty shot and Cristobal Huet finished with 35 saves for the Canadiens (29-21-6), who have lost back-to-back games and four of their past five.
Montreal went 0-for-6 on the power play while Ottawa finished 1-for-8.
The teams meet again Saturday night at the Bell Centre.
Canadiens coach Guy Carbonneau reunited the line of Saku Koivu, Christopher Higgins and Michael Ryder. It was a combination that served Montreal well in the early part of the season, but it was the Senators who took the lead 4½ minutes into the game.
Chris Neil sidestepped a check from Aaron Downey in the neutral zone and hit Phillips with a lead pass. Huet got a piece of Phillips' drive from the top of the faceoff circle, but the puck rolled off the tip of the goaltender's glove and in.
It was the seventh straight game in which the Canadiens have allowed the first goal.
Montreal then proceeded to give up a goal just 56 seconds into the second as Spezza found Heatley in the slot as Heatley notched his 32nd goal of the season.
Schaefer took a pass from Daniel Alfredsson and beat Huet from close range during a power play later in the period.
Latendresse gave the Canadiens hope when Phillips pulled him down on a breakaway with 2½ minutes remaining in the second. He scored on the ensuing penalty shot and Phillips also received a high-sticking minor on the play from referee Rob Shick, but Montreal couldn't convert with the man advantage.
Spezza added a goal with 1:31 remaining in regulation for good measure.
Notes: Bill Comrie, the father of Senators centre Mike Comrie and founder of The Brick chain of furniture stores, is scheduled to be awarded the Order of Canada by Gov. Gen. Michaelle Jean on Friday. ... Canadiens defenceman Andrei Markov, who's day-to-day with a knee injury, sat out the game. ... Montreal also scratched blue-liner Craig Rivet.