Bunting made it 3-1 with a redirection on the power play at 10:42 of the third period. It was his sixth goal in eight games this season.
Larsson cut it to 3-2 at 13:16, skating down the slot after getting a loose puck and beating Grubauer over his blocker.
"It was good to see the group stick together," Coyotes coach Rick Tocchet said. "We played good tonight. We deserved better. I liked our battle."
Rantanen scored into an empty net with 1:57 left for the 4-2 final.
"Probably some things we were not sharp enough," Rantanen said. "There are some things we could've done better, so maybe we lost focus a little bit."
The Avalanche were outshot 14-5 in the third period.
"We gave up some pretty high-quality chances, and 'Grubi' bailed us out like he usually does," Makar said. "Fortunately for us, he was having a pretty good night. We know the areas we can clean up, but I think for us it's just another learning curve. We didn't want to let them back in the game like that, but I thought we showed resiliency when it got close and we started to pick it up again."
NOTES:Bednar said forward Carl Soderberg, who was acquired in a trade with the Chicago Blackhawks on Monday, will join the Avalanche in St. Louis on Tuesday and would be available to play Wednesday against the St. Louis Blues. Soderberg played four seasons with the Avalanche from 2015-19. … Rantanen reached 300 points in the NHL. He has 124 goals and 176 assists in 323 games.