Knuble had two goals and an assist, and Backstrom had a goal and two assists for the Capitals. Knuble has 11 goals in his last 12 games and four in his last three.
That was enough to make up for a quiet night by Washington's two leading scorers: Ovechkin and Semin each had an assist for the highest-scoring team in the NHL.
"Alex is the best player in the world and Nick's climbing the ladder. I've just been able to find a way to play with these guys and complement them," Knuble said. "We're clicking."
The winning streak is the second-longest in franchise history, just one short of the 10 straight won by the 1983-84 team. Washington has won 12 times in January to tie the team record for a month, set in December 1984.
The Capitals, who lead the NHL in goals, have outscored the opposition 44-19 during their nine-game run.
"It's fun, but it's also a very businesslike atmosphere in here," Schultz said. "This is kind of the way we expect ourselves to play each night; we'll try to keep it rolling as long as we can."
Michal Neuvirth had 35 saves for Washington, 20-3-3 at home.
"I don't think we had our best game tonight," Capitals coach Bruce Boudreau said. "We gave up way too many chances, but Neuvirth was outstanding. When you have good goaltending, sometimes you overlook your mistakes."
Stephen Weiss got the lone goal for the Panthers, who simply didn't have enough weapons to outscore the Capitals.
"They have such gifted goal scorers that it doesn't take them much time to get a shot off and score," winger Cory Stillman said.
Washington is 5-0 against the Panthers this year with one game left in the lopsided series.
"Some of the decisions we made with the puck weren't very good," Florida coach Peter DeBoer said. "Against a team like that, unless you bring your A-plus game, they're going to make you look bad. And that's what happened."
The Capitals got a scare when standout defenseman Mike Green had to be helped off the ice after colliding with Dmitry Kulikov during the pursuit of a loose puck. The injury was diagnosed as a bruised thigh, and Capitals coach Bruce Boudreau said Green could be available for Sunday's game against Tampa Bay.
Washington needed less than 8 minutes to get its offense cranking. With Florida's Bryan McCabe in the penalty box, Backstrom got his 22nd goal by stuffing a rebound past Vokoun for a 1-0 lead.
But Florida tied it at 4:22 of the second period when Steven Weiss scored his team-high 20th goal of the season off a pass from Stillman.
Washington moved back in front just 25 seconds later. Ovechkin took a shot that tipped off the skate of Knuble, who was credited with a goal when the puck slid under Vokoun's pads.
"They're good at that," Stillman said. "They rebound quickly. If you score, they're going to come right back. Unfortunately, they did it in 25 seconds -- and that's the game-winner tonight."
The Capitals killed five penalties and are 25 for 26 over the last six games. ... Vokoun has started the last 14 games for Florida, going 7-5-2 in that span. ... Washington has outscored the opposition 67-36 in the first period.