The Islanders got regulation goals from Doug Weight, Tim Jackman and Andy Hilbert.
Danis stopped 36 shots for the Islanders, who lost their third straight after a four-game winning streak.
Wayne Simmonds, Anze Kopitar and Alexander Frolov scored for the Kings. Jonathan Quick, who started his eight straight game, turned aside 22 shots.
Los Angeles opened the scoring just 2:08 into the game.
Simmonds, in the left circle, took the puck from teammate Brad Richardson and ripped a quick wrist shot past Danis' short side.
The Islanders tied it at 4:53 when Mike Comrie fed Bill Guerin alone in the slot. Guerin waited for Quick to make a move, and then pushed a soft back-pass to Weight, who immediately beat Quick to the glove side.
Jackman put the Islanders up 2-1 at 4:20 of the second period with a goal from a nearly impossible angle. Standing along the goal line to Quick's left, Jackman threw a wrist shot toward the net that hit the post and deflected in.
The lead lasted just 67 seconds, as Kopitar tied it by finishing a 2-on-1 with Patrick O'Sullivan.
Hilbert got a quick wrist shot off in the low slot and beat Quick to put the Islanders back on top at 9:50.
Frolov made it 3-3 at 6:41 of the third period when he banged in a rebound with 2 seconds left on a Los Angeles power play. Frolov leads the team with 22 goals.
The Islanders didn't register a shot in the period until Sean Bergenheim sent one on Quick with 7:16 left.
Notes: The Islanders have lost three straight to Los Angeles. ... The Kings wrapped up a five-game road trip (4-1), but will make two more visits to the East Coast this season.
