Kessel's first goal came with the Leafs trailing 2-0 in the second period and his next tally gave Toronto a 3-2 lead later in the second.
Kessel completed his second hat trick as a Maple Leaf with another tally at 8:11 of the third.
Jonathan Bernier earned the victory with 23 saves.
Nick Bonino and Mathieu Perreault each scored for the Ducks, who lost for the first time since their 2013-14 season opener.
Jonas Hiller made 19 stops for Anaheim.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys