The two-time defending champion Lightning also lost Game 1 of the 2020 Cup Final but came back to beat the Dallas Stars in six games.
"The mindset is we're here to win a series and you don't know when that's going to come," Tampa Bay captain Steven Stamkos said. "Four games, five, six, seven, you never know. We've done a great job of making adjustments after losses. So, we'll look to do that."
The Avalanche came out strong in the first period despite not playing since June 6, when they won Game 4 of the Western Conference Final to finish off a sweep of the Edmonton Oilers.
Landeskog gave them a 1-0 lead at 7:47 of the first period. Rantanen's shot from the left face-off circle got through Vasilevskiy, and Landeskog got behind the goalie and put it in.
Nichushkin scored 1:36 later to extend the lead to 2-0 at 9:23.
"I hope I'm not alone, but I was pretty nervous all day and coming off of warmups the fans were amazing," said Landeskog, the Colorado captain. "You're trying to enjoy the moment as much as you can but you're human and the nerves are there. That's OK, you just have to deal with it and I thought as a team we did a good job of that tonight."