Alfredsson, who missed 11 games because of a separated left shoulder, and Chris Phillips scored 1:22 apart to give Ottawa a 3-2 lead -- its second of the game -- 5:07 into the second.
"It's a great boost for us, not only his skill but that's what his leadership is, by going out there and leading by example, working hard every time he's on the ice and being reliable," Phillips said. "That's what he's all about and it's a big mental boost for everyone to see him back in there."
Mike Brodeur stopped 30 shots in his third career start and second in a row. Brodeur beat the Rangers 2-0 in New York on Thursday for his first shutout.
Brodeur, who improved to 3-0, was called up from Binghamton of the AHL and pressed into action two nights earlier when both Ottawa goalies were unable to start in New York. The Senators lost No. 1 goalie Pascal Leclaire for a week with a concussion after he was struck by Mike Fisher's slap shot in practice Thursday. Backup Brian Elliott was ill.
"I'm floating right now, that's for sure," said Brodeur, who got the win in his NHL debut Dec. 19 in a 4-1 victory over Minnesota.
Alfredsson got his third point with his second assist as Mike Fisher scored into an empty net with 25.2 seconds remaining.
"It was a lot of fun to be back playing, obviously, and in a building like this as well," said Alfredsson, who set up Smith's short-handed goal in the first. "Our penalty killing and goaltending were really solid and some timely goals for us as well. We scored at the right time and then I thought we weathered the storm really well."
Ottawa's consecutive wins follow a five-game losing streak.
"It's so important to try and win in regulation and not make it just a one-point game on the other team," Alfredsson said. "We're very happy and hopefully we can keep this little streak going."
"I just wish we wouldn't have left it to a game where we had to tie it up in the last two minutes," Canadiens left wing Mike Cammalleri said. "I thought tonight was our game to come out and compete and win at home and we didn't do that."
Carey Price made 24 saves for Montreal. His record fell to 11-16-3.
Price had little chance on Phillips' goal 5:07 into the second. Phillips was credited with his fifth of the season after his slap shot struck Plekanec's stick on its way past Price.
"I'll take it," Phillips said. "You know, you've got to be lucky to be good."
Alfredsson had tied it at 2 moments earlier with his first goal since Nov. 28. The Ottawa captain, who had not scored in his previous 13 games when he was injured in an 8-2 loss in Pittsburgh on Dec. 23, got his 10th goal at 3:45 when he backhanded a rebound of Matt Carkner's shot past Price.
"It felt great," Alfredsson said. "I was able to get a rebound and move a little bit laterally and slide it 5-hole. It was a great feeling and a little bit timely for us as well."
Smith opened the scoring with a short-handed effort 11:26 in for his first goal in five games, including four this season. Recalled from Binghamton of the AHL on Jan. 8, Smith took Alfredsson's pass after the Canadiens turned over the puck on the power play and drove in to fire a wrist shot past Price into the top left corner from the top of the right faceoff circle.
"It's unreal, especially to score here in Montreal in front of all these fans," Smith said. "It's a pretty special building."
Pouliot scored for the second straight game at 12:49 to tie it at 1.
Plekanec gave Montreal a short-lived 2-1 lead with his 11th goal 2:05 into the second. The Czech center's sharp-angle shot from the right corner caught Brodeur by surprise and went in off the goalie's legs.
"It came off the wall real quick -- I didn't get to my post quick enough, you know, I was kind of looking through skates," Brodeur said. "It did catch me by surprise. I don't want to give that one up any other time, that's for sure."
- Smith, who appeared in one game for the Senators last season, was selected 79th overall by Ottawa in the third round of the 2008 draft.
- Pouliot has six goals in his last nine games.
- Plekanec, who leads the Canadiens with 46 points, had gone five games without a point.