Ekman-Larsson blasted a high slap shot from the point 56 seconds into OT that beat Jaroslav Halak and improved the surging Coyotes to 13-4-2.
David Moss and Mikkel Boedker scored in regulation for Phoenix. Smith faced 39 shots, including 13 in the third period.
One of the Blues third-period shots resulted in a game-tying goal by Roman Polak at 2:49. Maxim Lapierre opened the scoring at 5:53 of the first period.
Halak made 16 saves for the Blues, who had their winning streak halted at three games.