Anze Kopitar scored the only goal of regulation for the Kings, who snapped a three-game slide.
Quick stopped 21 shots for the 171st win of his career, tying Rogie Vachon for most wins by a goaltender in franchise history.
Joel Ward had the only goal and Halak stopped 27 shots for the Capitals, who had a three-game winning streak stopped.
The only goal of the first period went to Los Angeles at the 14:09 mark. Justin Williams had dumped the puck into the Washington end from his own blueline and Gaborik caught up to it in the left corner, sending it back to the circle where Kopitar one-timed it in for his 22nd of the season.
Neither side got on the board in the second period, as Halak stopped 11 shots while Quick turned away eight.
Washington tied the game at 12:24 of the third period when Evgeny Kuznetsov skated around the right wing to the side of the net and sent the puck over to the left circle where Ward got his second shot in for his 22nd of the year.
The Capitals had a power play in the overtime, but were unable to capitalize and the game was decided in the shootout.