Craig Smith, Nick Bonino, Filip Forsberg and Miikka Salomaki also scored for Nashville. Pekka Rinne made 26 saves, and 12 players had at least one point for the Predators.
T.J. Oshie scored twice and Alex Chiasson also had a goal for Washington, which had won two consecutive games.
Smith scored the first goal at 11:48 of the opening period. On a delayed penalty to the Capitals, he redirected Fiala's shot past Capitals goalie Braden Holtby for his sixth of the season.
The goal came on Nashville's 12th shot of the period. Washington had not registered a shot on Rinne to that point. The Predators ended the first with an 18-3 shots advantage.
Bonino made it 2-0 at 17:43. Standing just to Holtby's right side, Bonino tipped Roman Josi's wrister from the top of the left circle for his second goal of the season.
Bonino missed Nashville's previous 11 games with a lower-body injury.
The teams combined for seven second-period goals, including five in the span of 4:52. Washington briefly tied the game early in the second after Oshie and Chiasson scored 1:59 apart.
Nashville regained the lead for good at 6:28 on Forsberg's goal.
In the left faceoff circle, Forsberg stole the puck from John Carlson and sent a wrist shot toward the Washington net. The puck glanced off the skate of Capitals defenseman Brooks Orpik and by Holtby.
It was Forsberg's 100th NHL goal. Nashville acquired Forsberg in a 2013 trade-deadline deal that was a bust for the Capitals, who netted Martin Erat and Michael Latta in return.
Holtby made 19 saves and was replaced by Philipp Grubauer at the start of the third period. Grubauer turned aside all six shots he faced.
