The Kings (22-20-4) have lost three in a row and four of their past six games.
Jeff Carter and Drew Doughty scored in the first 4:06 of the third period to erase the Islanders lead. Carter's goal, a power-play goal at 37 seconds, ended New York's shutout streak at 166:44. Doughty scored 3:29 later on a shot that deflected in off Leddy.
However, Derek Forbort went to the penalty box for holding Chimera at 9:20 of the third period, and Lee scored on the deflection 10 seconds later.
Lee has four goals in two games against the Kings this season.
"They scored those two power-play goals [the] same way, where they're between the goalie and the defenseman in front," Kings coach Darryl Sutter said. "We gotta stop the puck and win a battle."
The Islanders had a 2-0 lead despite getting outshot 27-18 through two periods. They outshot the Kings 18-9 in the third. Tavares scored an empty-net goal at 19:17, his eighth goal in the past five games.
"Just our composure, we didn't panic," Berube said. "We gave up two quick goals, but we didn't see anything changing. I think we actually picked it up after we gave up those two quick goals. They're a good team, really big, and that's what we had to do, outwork them."
Chimera gave the Islanders a 1-0 lead on their first shot 2:30 into the game. Lee made it 2-0 lead by scoring on a rebound from the left post after Kings goalie Peter Budaj (32 saves) stopped Tavares' shot from the top of the left circle.