On the night he was celebrated for reaching 1,000 career points last month, Leon Draisaitl recorded a pair of goals in the first and second periods to give the Oilers a 2-1 lead 1:07 into the middle frame, but the Kings continued to compete hard before tying the game a few minutes later through rookie Andre Lee.
Under seven minutes into the final frame, the Kings had their first lead when Alex Laferriere scored on a deflection from the left circle, before Connor McDavid stepped up on a five-on-three before the period's midway mark to set a new career-high point streak of 18 games by reaching 30 goals this season.
McDavid now has 19 goals and 23 assists over his 18-game point streak, the longest point streak by any player in the league this season, and the captain has goals in four straight games, tallying six over that span.
With the game tied at 3-3, an exciting overtime period saw McDavid have a goal disallowed for goaltender interference after he walked Drew Doughty one-on-one in the zone, made a hard cut to the net and had the puck go off his body and the post, crossing the goal line as he was pushed into Anton Forsberg.
In the shootout, Adrian Kempe scored the only goal while Forberg stopped all three shots he faced from McDavid, Draisaitl and Nugent-Hopkins.
"I thought we had looks to win this game," McDavid said. "I don't know what it is. We really gotta find a way to put together a streak. I keep on saying it's an important stretch for us, so we gotta put a string of wins together."