Mark Streit netted the game-winning goal 96 1.
Andrei Loktionov lit the lamp in regulation for the Kings, who are 1-4 on their six-game road trip and have tallied just four times during the stretch. Jonathan Quick made 23 saves.
On the game-winner, Streit skated down the middle of the ice and eluded Milan Jurcina in the high slot before snapping his backhander past Quick.
The Islanders struck first at the 6:52 mark of the opening period. Mark Eaton's slap shot from the top of the left circle was deflected in front of Quick. Grabner pounced on the loose disc in the crease and wristed it into the net.
Los Angeles tied the score on Loktionov's first tally of the season, 5:20 into the second. Rob Scuderi sent a slap shot on net from the top of the left circle and Loktionov put home the rebound.
Quick stopped 12 shots while Nabokov made 11 saves in the third period to send the game into overtime.
The Kings' road trip ends in Dallas on Sunday...Both teams were 0-for-2 on the power play...Grabner's goal was his 15th of the season...Los Angeles ranks last in the NHL with 116 goals.