In Los Angeles, center Mark Johnson's second goal of the game, which came with 7:49 remaining in the final period, broke a 3-3 tie and won for Hartford.
Johnson took a pass from Ray Neufeld, went around Los Angeles defenseman Mark Hardy, faked goalie Mike Blake off his skates and tucked the puck into the net to break a deadlock that had existed since midway through the second period.
Neufeld added an empty-net goal with 26 seconds left.
Greg Adams also scored two goals for the Whalers (2-4-2). Johnson, a standout for the United States in the 1980 Olympic Games, has four goals this season and Adams three.
The Kings (4-2-2) got off to a fast start. Marcel Dionne connected on a power play after 1:22 of play and Steve Bozek scored at 9:34.
But Johnson got his first goal of the game at 16:25 while killing a penalty. He found himself alone on a breakaway and scored on a 30-footer past Blake.
That made it 2-1 and the Whalers tied the score with 33 seconds to go in the first period on Adams' first goal of the game, which came during a power play.
Adams gave the Whalers a 3-2 lead after 5:02 of the second period with his second goal, then rookie center Bernie Nicholls scored his ninth goal of the season on a power play at 9:14 to tie the game again.
Rookie Los Angeles defenseman Peter Helander suffered a fractured bone just above the left wrist early in the second period. Helander, 31, was injured in a collision away from the puck. A spokesman for the Kings said would be sidelined indefinitely.