Backes, playing in his 25th game, notched his third and fourth goals - three have come in the last three contests.
Bill Guerin and Dallas Drake also scored while Manny Legace made 20 saves. Lee Stempniak had two assists for the Blues, who improved to 11-11-6 on the road.
Rick Nash and Alexander Svitov had goals for Columbus, which has dropped five of six. Nash scored only his second goal in 17 games.