Laviolette, who is 600-399-114 with 25 ties in 17 NHL seasons with the New York Islanders, Carolina Hurricanes, Philadelphia Flyers and Predators, joined John Tortorella (603-479-104 with 37 ties) of the Columbus Blue Jackets, who reached the milestone on Jan. 10.
"To be honest with you, the win itself as a single identity tonight means a lot," Laviolette said. "Not the 600, but just the game itself. The milestones, they kind of come and go, but tonight for us and our group, it was just an important win coming off a couple of tough games.
[WATCH: All Predators vs. Avalanche highlights]
"We're on the road, we know [Colorado is] a lot to handle. To me, the game itself was important. I'm happy for the guys because of that. (No.) 600 just happens to fall on this night."
Nick Bonino, Viktor Arvidsson, Roman Josi and Ryan Ellis scored, and Pekka Rinne made 35 saves for the Predators (29-18-4), who had lost two in a row.
"It's awesome," Bonino said of Laviolette's milestone win. "He's a great coach and won at all levels. It's a pleasure to play for him. USA hockey is really big right now and he's one of the reasons why. Everyone in this room, especially the Americans, are thrilled for him."
Alexander Kerfoot scored, and Semyon Varlamov made 23 saves for the Avalanche (22-19-8), who have lost two of their past three games and are 3-9-2 in their past 14.
"I have no problem with the way we played today," Avalanche coach Jared Bednar said. "We made a couple mistakes, they capitalized. They made lots of mistakes, too. We didn't capitalize. To me, the difference was Rinne."
Video: NSH@COL: Arvidsson uses speed to score on wraparound
Rinne kept the game 0-0 when he made the save against Matt Nieto with his right pad on a penalty shot at 3:30 of the second period.
"I think if I'm able to get that by him, it's a different game, a different outcome," said Nieto, who hasn't scored since Dec. 8 (20 games). "I tried, it didn't work out."
Bonino gave Nashville a 1-0 lead at 5:01 of the second, beating Varlamov five-hole following a turnover by Nikita Zadorov for his 100th NHL goal.
"We scored first, that's huge for our team," Bonino said. "We didn't let them come down and dictate player early. We know how fast they are. This is one of the more complete games from [Rinne], he was huge when he had to be."
Video: NSH@COL: Bonino opens scoring with 100th NHL goal
Arvidsson made it 2-0 at 6:35. After racing down the right side to retrieve a stretch pass from Filip Forsberg, he faked a shot and scored on a wraparound. He has 11 goals in his past 12 games.
"They win a race," Bednar said. "I don't like the goal, that he was able to skate it around and wrap it around. [Defenseman Ian] Cole could have broken off it just a split-second earlier to make the net front. I'd like to see [Varlamov] get over there. Guy's going down below the goal line, he's not bringing it to the net at that point. I think both players could have reacted differently to it."
Kerfoot cut it to 2-1 at 16:43 on a redirection of Samuel Girard's pass, but Josi scored 1:15 later off a pass from Austin Watson into an open net on a 2-on-1.
Video: NSH@COL: Josi buries Watson's feed on the rush
Ellis extended the lead to 4-1 with an empty-net goal at 17:07 of the third period.
Nashville limited Colorado's top line of Gabriel Landeskog, Nathan MacKinnon and Mikko Rantanen to a combined nine shots on goal.
"Those guys are so dangerous," Rinne said. "You know they're going to have a couple good looks and they did tonight. We did an extremely good job playing against them."
They said it
"More than anything, for the players and the coaches and the staff, and everybody that's a part of it, I'm just thankful for not only this team, but teams previous. It's been an accumulation of four different teams. I think I'm just fortunate to be in the game and to stay in the game and have the greatest job in the world." -- Predators coach Peter Laviolette on his 600th NHL win
"There's some positive things, but it was tough to find the back of the net. The first two periods we played really good hockey. We were creating a lot of chances. [Pekka] Rinne played really good. Some of it is our fault, too." -- Avalanche forward Mikko Rantanen
Need to know
The Predators have won 12 of their past 13 regular-season games against the Avalanche. … Nashville went 0-for-3 on the power play and is 0-for-24 over its past seven games. … Bonino has eight points (five goals, three assists) in his past six games. … Nieto's penalty shot was the first for the Avalanche since Landeskog scored against the Washington Capitals on Nov. 16, 2017.
Predators: At the Vegas Golden Knights on Wednesday (10 p.m. ET; NBCSN)
Avalanche: Host the Minnesota Wild on Wednesday (9:30 p.m. ET; ALT, FS-N, FS-WI, NHL.TV)
Video: Laviolette earns 600th win, Predators top Avalanche