Lee Stempniak, Kyle Turris and Scottie Upshall scored for the Coyotes, who dropped to 4-1-1.
Edmonton looked to win the game in regulation with a late 3-2 lead.
But the Coyotes sent the game to overtime with 1:33 left when Upshall poked the puck past Martin Gerber while sliding in on net after being hauled down.
The Coyotes depart for Europe this weekend where they will next play an exhibition game in Riga, Latvia, before moving on to Prague in the Czech Republic to start the regular season against the Boston Bruins.
|Lee Stempniak (1) Wrist shot - ASST: David Schlemko (1), Taylor Pyatt (1)|
1 - 0 PHX
|Kyle Turris (1) Wrist shot - ASST: Petr Prucha (1), Scottie Upshall (1)|
2 - 0 PHX
|PPG - Sam Gagner (1) Backhand shot - ASST: Ladislav Smid (1), Gilbert Brule (1)|
2 - 1 PHX
|Alexandre Giroux (1) Wrist shot - ASST: Liam Reddox (1), Alex Plante (1)|
2 - 2 Tie
|Colin McDonald (1) Tip-in - ASST: Alex Plante (2), Ryan O'Marra (1)|
3 - 2 EDM
|Scottie Upshall (1) Wrist shot - ASST: Petr Prucha (2)|
3 - 3 Tie
|1||S. Gagner||K. Turris|
|2||D. Penner||M. Boedker|
|Magnus Paajarvi Hi-sticking - 2 min against Eric Belanger|
|David Schlemko Holding - 2 min against Magnus Paajarvi|
|Ryan O'Marra Hi-sticking - 2 min against Derek Morris|
|Taylor Chorney Fighting (maj) - 5 min against Vernon Fiddler|
|Vernon Fiddler Fighting (maj) - 5 min against Taylor Chorney|
|Taylor Pyatt Roughing - 2 min against Taylor Chorney|
|Alex Plante Holding - 2 min against Kyle Turris|
|Taylor Pyatt Hooking - 2 min against Richard Petiot|
|Kyle Turris Hooking - 2 min against Colin McDonald|
|Oliver Ekman-Larsson Holding - 2 min against Magnus Paajarvi|
|Derek Morris Hooking - 2 min against Ales Hemsky|
|Keith Yandle Roughing - 2 min against Ryan Jones|
|Scottie Upshall Roughing - 2 min against Magnus Paajarvi|