"Every point we get, whether it's one point or two points, it helps build a resume to make the playoffs," said Quick, who improved to 8-0 in shootouts this season. "We're just trying to get two points every time we're out. We got two points and that's all that matters."
Jarret Stoll gave the Kings a 1-0 lead with 5:52 left in regulation on Los Angeles' 24th shot. The Flames tied it 65 seconds later when Olli Jokinen slipped the puck past Quick on Calgary's 22nd shot. It was his 16th goal this season and sixth in 21 career games against his former team.
Stoll pulled Los Angeles even in the shootout after Alex Tanguay beat Quick, and Kopitar put the Kings ahead when he slipped the puck through Miikka Kiprusoff's pads.
"It was fun to see him go in like that and be fancy and score," Stoll said of Kopitar. "Kiprusoff's a world-class goalie. Kopie made a great move."
The Kings jumped two points ahead of Chicago into fifth place in the Western Conference playoff race.
"We've got some games in hand on that hockey club and we move up a little bit on the ladder," Los Angeles coach Terry Murray said.
Calgary's Curtis Glencross then shot wide of the right post to end it. With 85 points, the Flames are tied with Anaheim and Dallas -- one point behind Chicago and Nashville with seven games remaining.
Kiprusoff made 27 saves for the Flames, who were coming off a 5-4 overtime loss at Anaheim on Sunday. Calgary lost for the fifth time in six games following a 16-3-3 stretch in which Kiprusoff started every game but the first one and allowed more than three goals twice.
"It was a hard-fought game, it was like a game seven playoffs, you can't ask for anymore than that," Calgary coach Brent Sutter said. "Obviously it's important that we try to get two points, but the effort was there, we did a lot of really good things here tonight, and we come up a little bit short."
The Kings extended their streak of successful penalty kills to 35 by turning aside six Calgary power plays -- including one in the final 1:03 of overtime after a penalty for too many men on the ice. The franchise record is 46 straight, set in 2001-02 season.
"That was 20 guys out there, 40 guys out there, that put a heck of a performance on," Murray said. "That was intense, very much playoff-like, and a lot of good things on both sides. It was a fun game to play and a fun game to coach."
Material from wire services and team media was used in this report.