Biron, starting in place of the slumping Henrik Lundqvist, was severely tested late in the game as the Flames sought the equalizer but held tough, turning aside 31 shots in all for New York.
Biron notched his fifth win of the year, Dan Girardi collected a goal and an assist, and Brian Boyle also scored as the Rangers took their fifth win in seven games.
The struggling Flames were again led by Jarome Iginla, who scored his sixth goal in three games, but it wasn't enough as Calgary dropped to 2-8-1 in its last 11 contests.
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