Tanguay shot second for the Flames and recorded the only goal of the shootout.
Edmonton had goals from Magnus Paajarvi, Kurtis Foster, Jordan Eberle and Tom Gilbert, but remained winless in its past five games. Nikolai Khabibulin allowed four goals on 39 shots.
Calgary led 4-1 late in the second period but the Oilers rallied with a late-period goal by Eberle and two more goals in the third period. Gilbert tied it at 9:19 of the third period on a wrist shot.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys