Miller earned the road victory while coming off back-to-back shutouts in his previous two starts as the Sabres strengthened their playoff hopes with their first win in Vancouver since 1999.
A pair of first-period goals from Ville Leino and another from Brad Boyes chased Canucks goaltender Roberto Luongo, and Buffalo went on to become only the second team to hand Vancouver a regulation-time home defeat since Jan. 15.
The Sabres pulled to within two points of the eighth and final Eastern Conference playoff spot.
David Booth scored twice and and Zack Kassian also scored for NHL-leading Vancouver.
Luongo let in three goals on seven shots before being pulled. Cory Schneider entered and stopped 16-of-17 shots the rest of the way.
Reindeer recovered after escaping from Santa during lighting ceremony
Exploding whale video goes viral on Internet