The Canadiens, who got a pair from Guillaume Latendresse and singles from Alex Tanguay and Tom Kostopoulos, lost their fourth in a row. They remain tied with Carolina for seventh place with 81 points -- one ahead of ninth-place Florida -- in a tight race for the final Eastern Conference playoff spots.
Montreal is 1-2-2 since Gainey assumed the head coach's duties after firing Guy Carbonneau on March 9.
"Our team had been struggling for quite a while and I think the idea of changing the position of the coach was one to attempt to increase our chances in the last 16 games of the season, and I think we can judge how that goes when we finish our final game," Gainey said.
Price allowed four goals on 15 shots before he was replaced early in the second. The sophomore goalie has won four times in 18 starts since returning from an ankle injury prior to the All-Star game.
"I've got to take responsibility. I can't be letting goals in," Price said. "It's a group effort but I've got to play better."
Brian Elliott stopped 28 shots and set a Senators rookie record with his seventh straight victory.
Despite the run, Ottawa sits 12th in the East and is on the verge of missing the playoffs for the first time since 1996.
"Every time you put your gear on, it doesn't matter what the situation is, you want to win the game," Ruutu said. "We don't really look at the standings, we just take it a game at a time and you never know, magic might happen, but it's not really something you worry about too much."
Jaroslav Halak made 23 saves after taking over for Price following Ruutu's highlight-reel goal that made it 4-2 early in the second.
"It just felt like the opportune time to try to get the momentum of the game stopped by changing the goalie, and see if we could get things stopped and perhaps re-enter the game," Gainey said.
Halak stopped Christoph Schubert on a breakaway and made a left toe save on Alfredsson before Latendresse scored his second of the game midway through the second to draw Montreal to 4-3.
"He faced four or five really difficult scoring opportunities and held us there," Gainey said. "We did get back in the game and -- not enough, in time."
Foligno scored with the man advantage 2:55 in after Latendresse opened the scoring 2:04 in with his first goal in two games since returning from a shoulder injury.
Spezza scored Ottawa's second straight power-play goal 16:44 into the first before adding his second goal -- his 27th of the season -- on a deflection that made it 3-1 at 17:36.
He picked up his third point of the game with an assist on Alfredsson's goal 14:34 into the second that put Ottawa up 5-3.
Montreal closed within one three times, including Kostopoulos' ninth goal late in the second, without getting the tying goal.
"We have to stop playing catch-up hockey," Latendresse said.
Tanguay, who had the flu and missed Tuesday night's 4-3 shootout loss to the New York Rangers, scored 48 seconds into the second to draw Montreal within 3-2.
Ruutu answered moments later to chase Price, who made 11 saves. The pesky Finnish forward drove the right side and put the puck between his legs before putting a backhand into the top right corner that left the Canadiens goalie looking over his left shoulder while the Senators celebrated restoring their two-goal lead.
"It's pretty hard for a forward to beat the D one-on-one so I tried to make him commit a certain way and get a clear shot off," Ruutu said. "There wasn't much to shoot at so I just tried to go high, glove side, and it went off the post and in."
- Tanguay has two goals in six games since returning from a shoulder injury that sidelined him for two months.
- Elliott improved to 14-4-3 in 25 games since he was called up from Binghamton of the AHL in January.
- Jani Hurme won six straight games for Ottawa during his rookie season in 2000-01, and Ray Emery matched the streak as a rookie in 2005-06.
- Senators LW Dany Heatley scored five of Ottawa's nine goals overall against Montreal through the first four games of their season series.