The Coyotes had grabbed a 3-2 lead with 5:54 left in regulation on Antoine Vermette's goal, but they couldn't hold the advantage as Cody McLeod sent the game into overtime with a shot through Mike Smith's legs 2 1/2 minutes later.
In overtime, Phoenix's Keith Yandle was called for slashing and the Avs went on a power-play. O'Reilly ended the game with a snap shot from the right circle that beat Smith cleanly.
Andre Benoit supplied a goal and two assists and John Mitchell helped out with a goal and an assist for Colorado, which won a second straight contest following a three-game skid.
Semyon Varlamov stopped 41 shots for the victory.