Pierre Engvall and Jean-Gabriel Pageau scored for New York (34-27-8), which has lost its past two games after a 4-0-1 stretch. Ilya Sorokin made 32 saves.
"It didn't go as planned there in the second," Engvall said. "Obviously, it's something we want to do better."
The Islanders remained two points behind the Pittsburgh Penguins for the first wild card into the Stanley Cup Playoffs from the Eastern Conference. The Penguins lost 6-4 to the Montreal Canadiens on Tuesday.
Engvall gave New York a 1-0 lead at 11:45 of the first period. He chased down Ryan Pulock's dump in and scored with a wrist shot from the high slot that went in off Korpisalo's glove.
Lizotte tied it 1-1 with a redirection of Sean Walker's shot from the left point at 1:54, and Doughty gave Los Angeles a 2-1 lead at 6:06 with a one-timer from the left circle during a two-man advantage.
Iafallo made it 3-1 at 7:06 on the power play, tapping a loose puck into an open net after Viktor Arvidsson hit the post.
"Let's face it, we didn't reinvent the power play," Kings coach Todd McLellan said. "We just got a little sharper, a little faster. … Today we moved the puck a little quicker, and (against) a pretty good penalty kill on that squad."