Rantanen has 27 points (eight goals, 19 assists) in the streak and leads the NHL with 56 points (15 goals, 41 assists).
Gabriel Landeskog gave the Avalanche a 5-4 lead at 16:40 of the third period on a redirection of Erik Johnson's point shot, and Nathan MacKinnon scored an empty-net goal at 18:37 to make it 6-4.
WATCH: [All Stars vs. Avalanche highlights]
"We were confident," said MacKinnon, who also had three assists and is second in NHL scoring with 52 points (21 goals, 29 assists). "We let them back in it to make it 4-4, but it's encouraging. It's kind of like last time we played them, we won it late. It'd be nice to just close them out earlier than what we did, but it was nice to end the losing streak."
Landeskog scored twice, Matt Calvert scored and Semyon Varlamov made 38 saves for Colorado (18-9-6), which had lost three straight.
"We wanted to get back on the right side with this (four-game) homestand," Landeskog said. "It was an important two points and to get on the right track."