The Avalanche had a two-goal lead midway through the third period before back-to-back goals by Niklas Hagman and Brendan Morrow sent the game into overtime.
Jordan Leopold gave the Avs a lead again with a goal at 11:49 in the second before Zubov scored on the power play minutes later.
John-Michael Liles scored two power-play goals in the third period to give the Avs their short-lived two-goal lead.
Hagman scored at 10:51 in the third to cut the Avalanche lead to one.
Chris Conner had three assists for the Stars.