Jeff Halpern tied it at 1 in the second period with his eighth goal, and Plekanec put the Canadiens up 2-1 with his 17th at 5:46 of the third. Gionta, who scored twice in Tuesday's shootout win at Washington, made it a two-goal lead at 11:32 with his 19th.
"We knew it was going to be tough, you know, back-to-back games after five days off," Plekanec said. "It's not easy. You've got to stay focused and be patient and have that hunger in every battle.
"I thought we missed that a little bit through those first two periods but we stayed patient and came out strong in the third."
Auld, who blew a 4-0 lead in his last start, improved to 4-2 in eight games. The Canadiens improved to 9-2-3 in their last 14 games.
"It's tough to win on one goal," said Tomas Vokoun, who stopped 38 shots. "We did score at the end there, but it's been our problem all year. You can't expect to win 1-0 on the road, it's just impossible. I think we played hard, and that's all you can ask. They were just a better team."
Florida has only one win in eight games (1-3-4).
Auld earned his first win in two starts in Montreal, including a no-decision on Jan. 17 when he allowed four goals before being replaced by Carey Price in the Canadiens' 5-4 shootout win over Calgary.
"It feels great," said Auld, who signed a one-year, $1-million deal with Montreal to back up Price this season. "The last time I was standing here with you guys I was disappointed personally but we were able to get the win. It definitely feels good to come in here and show the fans that I can get the job done and deliver wins. That's what I've got to keep doing"
Halpern made it 1-1 at 4:50 of the second when he deflected P.K. Subban's point shot past Vokoun.
Plekanec, who assisted on one of Gionta's two goals in Washington on Tuesday, gave the Canadiens their first lead when his shot into traffic flipped into the air and found its way into the net.
Gionta scored his third goal in two nights when he beat Vokoun from the right side to give the Canadiens a 3-1 lead.
Weiss made it a tight finish when he jumped on a rebound and fired the puck into an open right side with 2:10 remaining.
Timmins gave Florida a 1-0 lead 7:30 in, scoring for the first time in two games after being called up from Rochester of the AHL on Tuesday.
"I wasn't really expecting the call," said Timmins, who made his debut in the Panthers' shootout loss at Toronto on Tuesday. "I've just been taking advantage and run with it. It's just amazing to be in the NHL."
- Timmins was chosen 165th overall by the Panthers in the sixth round of the 2009 draft, which was held in Montreal.
- Auld was 7-13-5 with one shutout and a 3.34 goals-against average in 27 games with Florida in the 2006-07 season.