The Rangers fell behind 2-0, and then racked up seven straight goals in the first and second periods before Columbus got its last two scores.
Artem Anisimov, Michael Del Zotto and Matt Gilroy contributed the other New York goals and Gaborik added two assists.
Winning goalie Henrik Lundqvist turned back 26 shots. Steve Mason stopped 14 for Columbus, but after giving up four goals he was replaced by Mathieu Garon, who blocked 12 of 15 shots.
2014: The Year in Music [PHOTOS]