Nolan's first goal was a tip-in on a power play with 12:37 remaining in the period. His second, on a rebound shot, came just over 3 minutes later.
Backstrom finished with 32 saves in his fourth shutout of the season.
Minnesota has won two of three games and ended a six-game losing streak on the road.
Peter Budaj stopped 35 shots in the Avalanche's third straight defeat.