Nichushkin scored at 9:12 of the third period to cut the Predators' lead to 3-2. But Josi's power-play goal from the slot at 12:19 of the third made it 4-2.
Mattias Ekholm scored an empty-net goal at 18:12 for the 5-2 final.
The Predators were coached by Karl Taylor, coach of their American Hockey League affiliate Milwaukee.
"This team has got the right energy, the right mentality," Taylor said. "We just tried to come in and not get in the way, make sure we just rode the wave they're on right now. Add a few things here and there, make sure they had direction, make sure we executed the game plan properly."
NOTES: Forsberg had his 24th three-point game, passing Martin Erat for the most in Predators history. … Kuemper, defensemen Cale Makar and Devon Toews, and forwards J.T. Compher and Andre Burakovsky are the Avalanche players in COVID-19 protocol. … Emergency backup goalie Dustin Smith suited up for Colorado. … The Predators recalled forwards Rocco Grimaldi, Cody Glass, Cole Smith, Mathieu Olivier and Kole Sherwood from Milwaukee. ... The seven Nashville players in COVID-19 protocol: forwards Nick Cousins, Ryan Johansen, Mikael Granlund, Philip Tomasino, Michael McCarron and Matt Luff, and defenseman Ben Harpur. … Coach John Hynes, assistants Dan Lambert, Dan Hinote and Todd Richards, and goaltending coach Ben Vanderklok are also in COVID-19 protocol for the Predators.