Colorado lost its fourth in a row and has dropped eight of its last 11 games. Minnesota has won three of four.
It was the second shutout of the campaign for Giguere, who did not have any last season. He has 36 in a 14-year career spent with five teams.
Zanon scored the lone goal 6:04 into the first period, putting a wrist shot past Niklas Backstrom.
Zanon has just two goals this season. Thursday's goal was his 11th in 421 NHL games over seven seasons.