The Coyotes halted a six-game losing streak.
Mikael Tellqvist stopped 38 shots in what was the finale of a four-game road trip.
Phoenix center Olli Jokinen, the team's second-leading scorer, left the game in the first period with an unspecified injury and did not return.
Steve Mason suffered the loss, allowing three goals on 25 shots. Columbus has dropped three out of four.
Three of the Coyotes' nine wins this season have come against Columbus.
2014: The Year in Music [PHOTOS]