Rantanen scored on a breakaway to make it 2-1 at 5:13 of the second.
Silfverberg gave the Ducks a 3-1 lead when he scored his 15th goal at 2:51 of the third period after receiving a centering pass from Cogliano while charging through the slot.
Korbinian Holzer made it 4-1 at 12:13 when he scored his first NHL goal since Feb. 9, 2013, for the Toronto Maple Leafs.
Defenseman Cam Fowler put the Ducks ahead 5-1 with his NHL career-high 11th goal with 2:25 remaining.
"I liked our game in the second and third periods," Fowler said. "We got the win, and that's all that matters heading into a big road trip."
The Avalanche had three power plays in the first period and totaled six shots on goal with the man-advantage, but they couldn't get the puck past Gibson. Colorado was 0-for-4 on the power play.
Avalanche defenseman Fedor Tyutin was a late scratch because of a groin injury. Tyutin, fifth on Colorado in average time on ice (19:16), was replaced in the lineup by Patrick Wiercioch.