Cogliano's trio of goals all came in the second quarter and carried the Ducks to their sixth win in seven games.
Teemu Selanne scored an empty-net goal for Anaheim and Nick Bonino contributed assists on two of Cogliano's scores.
Ray Whitney gave Phoenix a 1-0 lead in the first period, but the second period belonged to Cogliano, who had eight goals coming into the game. He tied the score 1-1 on a wrist shot at 6:59 of the second and then put Anaheim in front with another wrister at 10:07. He completed the hat trick at 13:50.
Jonas Hiller stopped 25-of-26 shots for the Ducks.