"It's goal scoring by committee," Ottawa coach Paul MacLean said. "We're going to have to be that hard-working team that grinds out some goals. We did that tonight and we have to continue to do it."
Spezza missed his second straight game. He is day to day.
"We know we have to work hard every night and that's what we do," Alfredsson said. "When you've got good things going for you it's a lot easier obviously."
Down 4-1 in the third, the Canadiens made a desperate push to get back in the game, but Anderson made numerous point-blank saves, including two on Brandon Prust.
Anderson has been one of the Senators' best players since the start of the season.
"Guys are doing a terrific job in front of blocking shots and cleaning the garbage so I would say it's an overall solid effort by the guys in front of me," he said. "It allows me to do my job a lot easier.
"We're playing with a lot of confidence on our back end."
Neil made it 5-1 with a wraparound goal with just over five minutes left.
Ottawa grabbed control with a three-goal outburst in the second period.
"We took some penalties that we shouldn't have in the second and it cost us," Canadiens forward Brian Gionta said. "We laid off the pedal for about five, 10 minutes and they scored three quick goals and that's the difference in the game."
The Senators had a four-minute man advantage after Ryan White took a roughing penalty and was given an extra two minutes for arguing the call.
"He's a guy that works extremely hard for us and plays with passion," Gionta said of White. "He let it get to him a little bit."
Alfredsson put Ottawa in front 2-1 when he scored off a faceoff, and Zibanejad beat Budaj high stick side for his first NHL goal just over two minutes later. Zibanejad blew a kiss to the sky as part of his goal celebration.
Zibanejad was called up Monday morning and he's made the most of the opportunity, picking up points in his first two games.
"Obviously you want to get that first goal and get that out of the way and finally I got it," he said. "It's nice to see the puck go in and know you can score in this league."
MacLean has liked what he's seen out of Zibanejad and feels the 19-year-old is gaining confidence.
"I think he's even more relaxed than he was last year in the first nine games when he played with us," MacLean said. "I think he has a little more maturity and I think he's shown that he appreciates being in the NHL."
Phillips then got his second goal of the season. Zack Smith grabbed a bouncing puck and left it for Phillips, who jumped into the play and fired a wrist shot past Budaj.
The second period was much different than the first, which featured two fights and eight minor penalties that left both teams struggling to create any momentum.
The Canadiens took advantage of an early power play, with Plekanec jumping on a rebound and sliding it past Anderson. The Canadiens were 1 for 5 with the man advantage.
"Our special teams didn't work tonight," Canadiens coach Michel Therrien said. "Our power play often broke our momentum and our penalty kill wasn't very good. Special teams are key if you want to win hockey games."
O'Brien tied it at the eight-minute mark with his second in as many nights. Budaj took a shot off the helmet, which appeared to stun him for a moment, and O'Brien jumped on the rebound.