Schneider, in his 14th career start, was several minutes away from his first shutout for the streaking Canucks, who have won five straight games and extended their lead atop the Northwest Division to three points over Colorado.
Ryan Kesler, Henrik Sedin and Raffi Torres scored in the victory.
Peter Budaj allowed three goals on 36 shots for the Avalanche, who saw their two-game win streak halted and fell to 2-3-1 in their last six overall. Colorado, which had not played since Saturday, will continue its four-game homestand on Saturday against Dallas.
David Van der Gulik scored his first NHL goal in the losing effort.