New York earned at least the No. 8 position in the post-season, although the Rangers had to come from behind late to do it.
Brad Richards scored on the power play with 2:57 left in regulation to forge a 3-3 tie, and then Callahan touched off a celebration by scoring his 15th goal of the season. New York will compete in the playoffs for the seventh time in eight seasons.
Derek Stepan and Derick Brassard gave the Rangers a 2-0 lead in the opening period, but Carolina produced the next three goals to move in front.
Jiri Tlusty delivered two of those three scores, giving him 23 goals for the season.