The comeback win came in the second contest of a four-game swing for the Islanders through New York and New Jersey. They had lost the opener of the road trip in Buffalo on Tuesday.
Casey Cizikas scored his first goal of the season and Aaron Ness had the first of his career, both coming in the second period and giving the Islanders control heading into the final stanza.
Slava Voynov started the Kings' rally 5:34 into the third and Tanner Pearson also delivered his first career goal in his second NHL game to tie it.
Toffoli produced the game-winner on a slap shot that escaped Kevin Poulin.
Ben Scrivens, getting his first action in six games, picked up the win by making 23 saves. Poulin stopped 21-of-24 shots.