The Avalanche fell behind by a goal on three occasions and tied it each time, the last of those deadlocks forged when Paul Stastny scored with a minute to go in regulation.
Colorado won its second in a row. Carolina has suffered 11 overtime losses this season, the most in the NHL.
Tim Brent, Jiri Tlusty and Eric Staal each scored a go-ahead goal for the Hurricanes, whose 50 points are the fewest in the Eastern Conference.
Gabrial Landeskog, Milan Hejduk and Stastny all recorded a tying goal for Colorado.
Jean-Sebastien Giguere got the win by making 39 saves. All four Colorado goals came against Cam Ward on 33 shots.