Canadiens coach Guy Carbonneau was pleased with the job Koivu and fellow top line wingers Chris Higgins and Michael Ryder did in matching up against Philadelphia's top line, centered by Daniel Briere.
"Knowing Saku, Chris and Michael, they wanted that challenge and they did really well against him," Carbonneau said.
Higgins scored on a 5-on-3 at 16:42 of the third as the Canadiens remained undefeated through regulation in six games (5-0-1).
"They are a good team," Koivu said. "They have some skill, they have some size and they play hard. I thought tonight we had the jump and we played our style. We kept the tempo, we didn't turn the puck over at all and it seemed that we were able to create some offense, get the puck deep in their zone and get the cycle going. It was a good game."
Mike Richards and Scottie Upshall scored for Philadelphia, which lost for the third time in four games following a five-game winning streak.
Briere assisted on Richard's goal and was booed thoroughly by the sellout crowd of 21,273 throughout the game.
Briere, who spurned Montreal's contract offer to sign a free agent deal with Philadelphia, was booed when he stepped on the ice for his first shift a minute in, and again every time he touched the puck the rest of the way.
"They're fans who are loyal to their team," Briere said. "I can't get caught up in that. I'm sure they were waiting for this, and I was ready for it. I had fun with it and I just wish that we had come out with a better game, but you have to give the Canadiens credit, they played well."
Kostopoulos was one of three free agents, along with Bryan Smolinski and Roman Hamrlik, who signed with Montreal shortly after Briere passed up the team's offer.
"You never want to see anyone get booed but I can see he's a great player, and I can see the fans are disappointed," Kostopoulos. "He was born in Quebec and they'd like to see him here but our team's happy with who we got. We have the best captain in the league, I think the signings of Smolinski and Hamrlik were great, so I think we're happy with the guys in the room."
Martin Biron made 36 saves and stopped a penalty shot for the second game in a row.
Biron, who stopped Phil Kessel's penalty shot in Saturday's 2-1 win in Boston, denied Hamrlik, who put a backhand off the right post on his first career penalty shot 13:12 into the second.
Richards was in the penalty box along with Jason Smith for Higgins' goal after both were sent off following a big scrum in the wake of Richards' open ice hit on Kovalev.
"It wasn't an elbow, I think it was his shoulder, but it was definitely a hit to the head that had no impact on the game with 4:00 left," Carbonneau said. "I think that's the reason they have three guys suspended. If they continue playing like that, they will have some more."
Philadelphia's Ben Eager was given a game misconduct for his third-period fight with Kostopoulos. Montreal defenseman Mike Komisarek and Flyers left wing Scott Hartnell squared off in a spirited first-period bout.
Hamrlik drew an assist as Koivu opened the scoring with his fourth goal 8:53 in.
Richards was credited with his seventh goal when Philadelphia drew even on a power play at 16:50 as the puck struck both of Canadiens' defenseman Andrei Markov's legs before slipping past Huet.
Kovalev scored an unassisted power-play goal for the second straight game 7:28 into the second to give Montreal a 2-1 lead.
Kostopoulos made it 3-1 at 11:38 with a pretty, short-handed effort. Kostopoulos passed to Markov on a 3-on-1, and one-timed the defenseman's return pass beyond Biron for his first Canadiens goal.
"We've been talking about trying to go hard the other way on our PK if we get a chance," Kostopoulos said. "I was surprised Markov jumped up in the play -- he blew past their D and created the 3-on-1."
The Canadiens honored three of their legendary general managers in a pre-game ceremony. Tom Gorman, Frank Selke Jr., and Sam Pollock accounted for 17 of the team's 24 Stanley Cup titles over the course of their successive tenures between 1940 and 1978.
The Canadiens won two Stanley Cups under Gorman from 1940-46, six under Selke from 1946-64, and nine from 1964-78 under Pollock, who died of cancer on Aug. 15. ... A security guard was stationed outside the penalty box after some fans exchanged words with Smith and Richards.
Copyright by STATS LLC and The Associated Press
Arena: Bell Centre Location: Montreal, Quebec
Referees: Justin St. Pierre, Chris Lee Linesmen: Pierre Champoux, Brad Kovachik
Attendance: 21,273 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Saku Koivu (4)
Assists: Roman Hamrlik, Kyle Chipchura
Mike Richards (7)
(Power Play) Assists: Daniel Briere, Kimmo Timonen
Alex Kovalev (7)
(Power Play) Unassisted
Tom Kostopoulos (1)
(Shorthanded) Assist: Andrei Markov
Guillaume Latendresse (2)
Assist: Saku Koivu
Chris Higgins (5)
(Power Play) Assists: Mark Streit, Michael Ryder
Scottie Upshall (1)
(Power Play) Assists: Jeff Carter, Lasse Kukkonen