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.
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"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."
Alex 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."