The Blue Jackets rallied from a two-goal deficit in the final 4:05 to win for just the seventh time in 25 games this season.
Defenseman Nikita Nikitin scored his first goal of the season to bring Columbus within one and Nash tipped in a shot by Nikitin to send the game into overtime. Nash then beat Miikka Kiprusoff between the pads in the third round of the shootout.
Sanford was credited with 32 saves in helping Columbus snap a two-game skid. Kiprusoff made 30 saves.
Calgary had won its previous two games.
Swim Week Miami Beach 2014 [PHOTOS]