Patrik Laine, who is from Tampere, had a goal and an assist and a game-high seven shots on goal for the Blue Jackets (3-8-0), who have lost four straight, getting outscored 23-7. Elvis Merzlikins made 30 saves.
"Yeah, it was fun for the fans, not fun for us right now," said Laine, who was serving a slashing penalty when Rantanen scored the game-winning goal. "As a fan, and as a person, I'm happy for [Rantanen]; as a hockey player, not really."
Nathan MacKinnon had four assists for the Avalanche, and Alexandar Georgiev made 36 saves.
"It was really cool, all the kids [here] know us," MacKinnon said. "It's a long way to come, but when you see the happy kids and the happy people, it makes it well worth it for sure."
Avalanche forward Artturi Lehkonen (Piikkio, Finland) did not have a point or a shot on goal. Columbus goalie Joonas Korpisalo (Pori, Finland) did not play, but could start when the teams play here again Saturday (2 p.m. ET; NHLN, SN1, ALT, BSOH, SN NOW).
Logan O'Connor gave the Avalanche a 1-0 lead at 1:36 of the first period before J.T. Compher scored a power-play goal at 12:27 for a 2-0 lead.
Rantanen scored his first of the game to make it 3-0 at 35 seconds of the second period.
"I liked our effort tonight, I liked some of the things we did," Colorado coach Jared Bednar said. "It still wasn't a full 60 (minutes) from us. I thought the first period was real good from our guys, making sure we weren't give up a lot, scoring chances against. Second period I thought they outplayed us both on special teams and 5-on-5. Then in the third period, we stepped up and elevated. Really good effort from the guys."
A minute after Rantanen scored, Jakub Voracek made it 3-1 on the power play, deflecting a shot from Laine past Georgiev at 1:35. Columbus had not scored a power-play goal in its first 10 games this season (0-for-25).
"It was a good hockey game," Voracek said. "Even for the players, I am sure the other side felt the same way, it was an up and down hockey game, a lot of scoring chances, a lot of big saves. A lot of fight, a lot of hitting, lot of power plays. A fun hockey game to watch. Unfortunately, Colorado showed their experience."
Laine made it 3-2 at 7:16 of the second with wrist shot from the left face-off circle.
"It seemed like the crowd was enjoying the night, that is a positive thing'" he said. "I feel like they were cheering for both teams. It was fun to play, but right now it is not a good feeling."