McGinn saved Colorado with his second goal of the game in a contest that saw the Avalanche emerge with a win even though goaltender Semyon Varlamov gave up four goals on just 24 shots.
Peter Mueller scored in the second shootout round to give Colorado its third straight victory.
Colorado was one of four teams that began the evening tied for the eighth and final playoff spot in the Western Conference. The Avalanche jumped out of that pack since the other three clubs -- San Jose, Calgary and Los Angeles -- were idle.
Ryan Miller faced 42 shots and made 38 saves in the loss.
The game's first goal, credited to Buffalo's Marcus Foligno, was symbolic of the wild contest in that the puck bounced off his body as he was falling to the ice and then ricocheted off the stick of Colorado's David Jones into his own net.
Jones later made up for that misfortune by scoring with 52 seconds left in the first period to create a 2-2 tie.