I'm going to go out on a limb and say not letting the Avalanche powerplay operate at nearly 40% efficiency will be a key to winning.
Regular season large sample numbers give the Stars the special teams advantage. Equivalent PPs, Stars have the better PK, and the Stars take fewer penalties.
Playoffs change things. Unless a team is extremely stupid (like the Wild last season), the refs love to hand out equal numbers of PPs. Also, a team getting a hot PP can swing a series and even have it carry them on a playoff run. The Avs may have run a hot PP in the first round, but I bet the Stars PK is better equipped to deal with it.