Ovechkin and Backstrom scored first-period goals. Semin scored in the third, and Troy Brouwer added a fourth goal.
"I think we want to dictate our game, and we want to dictate our style and this system, so it was pretty cool," Ovechkin said.
Washington improved to 5-5 under new coach Dale Hunter. The Capitals are 6-1 in their last seven games against the Predators.
"When your top end guys score the confidence goes up for the rest of the bench," Hunter said. "The big guys scored."
Michal Neuvirth stopped 20 shots for the Capitals. Starting a third straight game for the first time this season, Neuvirth, who shut out Winnipeg on Thursday, has allowed three goals in that span.
"He's been solid," Brouwer said. "He makes it easy for us to play in front of him. We know if we do make a mistake he's going to be there for us."
Nashville lost for the first time in six games, and for the first time in 11 contests, had a game decided by more than one goal. The quirky 10-game streak was two shy of an NHL record, according to STATS LLC.
The Capitals grabbed a 2-0 lead in the first period. Ovechkin scored just his fourth goal in 18 games when he took a pass from Karl Alzner at the blue line, and in a blur, cleanly beat goalie Anders Lindback at 7:42 for his 11th goal of the season.
"It doesn't matter if Ovi scores, or anyone scores, the team is going right away. It all started with a good first shift," Brouwer said.
Backstrom netted his 12th at 15:51. He carried the puck behind the net, skated in front, and slammed a shot past Lindback. Washington dominated play in the first, jumping out to a 10-1 edge in shots.
The two-goal outburst in the period was a welcomed change for the Capitals, who had scored only one goal in each of their previous three games.
"I liked the first period more than anything," Hunter said. "We should have scored more."
The Predators' Sergei Kostitsyn broke Neuvirth's shutout bid 4:40 into the third period with his fifth goal.
"We didn't give enough run support for Lindy," Nashville coach Barry Trotz said. "When it was 2-1, we had lots of chances to tie it up, and we didn't."
Semin's seventh of the season made it 3-1 midway through the third and marked the first time this season he has scored in consecutive games.
"I told him after the second period, he has to shoot more," Neuvirth said.
Brouwer pushed the lead to 4-1 at 13:46.
Capitals RW Mike Knuble played in his 1,000th NHL game. The team honored him in a pregame ceremony, and each of his teammates wore a jersey with his No. 22 during warmups. ... The Predators recalled D Jonathon Blum and LW Blake Geoffrion from Milwaukee of the AHL. ... Nashville D Kevin Klein didn't make the trip because of the flu. ... Washington D John Erskine was a healthy scratch. ... Capitals C Marcus Johansson assisted on the last two goals.
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WASHINGTON, DC - DECEMBER 20: Fans of the Washington Capitals cheer on during warm ups of a NHL hockey game...