Stoll made a diving stab at the rebound of a Ryan Smyth shot and poked it past Ilya Bryzgalov, breaking a 3-3 tie less than 5 minutes into the final period.
The goal helped the Kings rebound after allowing three straight scores by the Coyotes, ruining a lead they had built when Justin Williams, Drew Doughty and Alec Martinez all scored in the first period.
Jonathan Quick stopped 23-of-26 shots and Smyth added two assists for Los Angeles, which broke a three-game losing streak and improved to 3-9-0 in its last 12 games.
Lee Stempniak scored twice and Martin Hanzal added a marker for Phoenix. which lost for the third time in four games.
Bryzgalov turned aside 29-of-33 shots.
2014: The Year in Music [PHOTOS]