Jonathan Quick tied Rogie Vachon for the most career victories by a Kings goaltender and stopped Alex Ovechkin, who leads the league with 46 goals, on the Capitals' second shot in the tiebreaker. Ovechkin is 2 for 15 this season in the tiebreaker and 25 for 83 in his career.
Quick made 21 saves, losing his shutout bid with 7:36 remaining when Joel Ward extended his goal-scoring streak to a career-best four games with his 22nd of the season.
The Capitals got a power play in overtime after Kings defenseman Robyn Regehr was sent off for hooking Marcus Johansson at the 53-second mark. But Quick robbed Troy Brouwer on a point-blank shot from the low slot during the ensuing 4-on-3 advantage.
Another of Quick's best saves came at 8:10 of the second period, when he stoned ex-teammate Dustin Penner with the heel of his glove at the last instant from the edge of the crease after leaving a bad rebound on Dmitry Orlov's slap shot from the left point.
The Kings, coming off their third consecutive one-goal loss following an eight-game winning streak, opened the scoring at 14:09 of the first period. Gaborik beat defenseman John Carlson to the puck after a long dump-in by Justin Williams and fed it in front to Anze Kopitar, who slid his 22nd goal between Jaroslav Halak's pads.
Sutter, who guided the Kings to their first Stanley Cup title in 2011-12 after Terry Murray was fired less than 2 1/2 months into that season, tied Montreal legend Hector ''Toe'' Blake for 17th place on the career list and is fifth among active coaches behind Joel Quenneville, Ken Hitchcock, Lindy Ruff and Barry Trotz.
Quick, who has spent his entire seven-year career with the Kings, is 171-115, with 11 overtime losses and 20 additional defeats that ended in shootouts. Vachon was 171-148 with 66 ties during his six-plus seasons with Los Angeles after he was traded by Montreal, and made all three of his All-Star game appearances during his time with the Kings.
Captain Dustin Brown returned to the Kings' lineup after missing two games because of a lower-body injury.
Halak made 27 saves for Washington, after stopping 43 shots on Tuesday in a 3-2 win at Anaheim. The eight-year veteran is 4-2-1 with a 2.13 goals-against average in seven starts since the Capitals acquired him in a trade with Buffalo on March 5 - just five days after the Sabres picked him up in a trade with St. Louis.
NOTES: Vachon finished his 16-year career with 355 wins, which was fifth all-time when he retired after the 1981-82 season. He has since dropped to 17th place. ... The Kings are 14-0 when scoring more than three goals. ... Williams played in his 200th consecutive game, becoming the 13th different player in franchise history to reach that figure - including Kopitar, who holds the club record with 330. ... The Kings are 16-20-6 when scoring fewer than three goals in regulation. Two of those wins were in overtime and six others have come in shootouts.