Laviolette became the 10th coach to reach the milestone and tied Mike Babcock for ninth on the wins list. Laviolette, coaching at Nashville for the first time since being fired as Predators coach Jan. 6, 2020, is 700-455-137 with 25 ties in 1,317 games.
The Capitals (27-15-9) had lost three of their past four games.
"The fact that it's Nashville and this is the last stop that we had … for me, the win was really good for our team," Laviolette said. "It's been a bit of a roller coaster. The Ottawa (Senators) game (a 4-1 loss Sunday), you don't feel good about it. You lose a game at home and you want to get back and win a hockey game. It ends up being Nashville. That's just the way it was kind of dealt out. It was a good win for our team."
Ovechkin scored his 30th and 31st goals of the season, and Ilya Samsonov made 33 saves for Washington.
Ovechkin scored 30 goals for the 16th time in his 17 NHL seasons, one short of the NHL record held by Mike Gartner, who reached the mark 17 times in his 19 seasons.
"If we play like that, we move the puck quick, we control the puck, it doesn't matter, me or somebody else is going to score," said Ovechkin, the Capitals captain. "I just try to do my job."