Stoll scored what turned out to be the game-winner at the 7:08 mark of the second period when he skated down the right side, took a pass from Dustin Brown and snapped it by Devan Dubnyk to make it 3-2 Los Angeles. Stoll added an empty-net goal later.
Drew Doughty, Marco Sturm and Anze Kopitar got the Kings' other goals. Jonathan Bernier made 24 saves for Los Angeles, which had lost seven of its previous eight games.
The Oilers' goals came from Andrew Cogliano and Dustin Penner. Dubnyk allowed four goals on 22 shots as Edmonton last for the third time in four games.