Callahan scored his 14th goal this season just 28 seconds into the game and Zherdev scored about 40 seconds later. Prucha and Gomez scored late in the period about two minutes apart.
The victory snapped their four-game losing streak.
Colorado averted a shutout when Ryan Smyth scored his 21st at 13:05 of the second.
Peter Budaj was beaten three times on nine shots before replacement Andrew Raycroft yielded three more goals on 20 shots for the Avalanche, who have lost nine of their last 11 road contests.