New York snapped a three-game losing streak with Evgeni Nabokov giving up only a first-period goal.
Tim Jackman scored Calgary's only goal 71 seconds into the game and Nabokov shut out the Flames for the remaining 58:49 while stopping 29 shots.
Jackman's goal was his first of the season and it took him 37 games to get it. He had a career-best 10 goals last season.
Calgary had won its previous four games. Kiprusoff made 31 saves for the Flames.