Jake Guentzel scored twice for the Penguins (25-14-6), who lost for the second time in their past 12 games (10-2-0). Casey DeSmith made 20 saves.
"I don't think we had our best game, but I did think we competed," Penguins coach Mike Sullivan said. "I think we beat ourselves in the second period, and that's unfortunate."
Quick made a sprawling glove save on Riley Sheahan at 4:17 of the second period before Alex Iafallo gave the Kings a 2-1 lead at 8:47 when Carter's centering pass hit him in chest and redirected in. The goal was his 10th of the season, surpassing the total (nine) he set as a rookie last season.
Kopitar made it 3-1 with a shorthanded goal at 16:05. It was the 10th shorthanded goal allowed by Pittsburgh, most in the NHL.
Sullivan said he is not considering going away from Pittsburgh's use of four forwards and one defenseman on the power play, but that those units need to be more responsible with the puck.
"I just think a lot of it is not what penalty kills are doing to us, it's what we are doing to ourselves," Sullivan said. "It's just carelessness. It's a lack of diligence in important parts of the rink. Even though we're on the power play, we have to have some conscience defensively, and it starts with our own puck possession."
Brendan Leipsic scored 49 seconds into the third period to extend the lead to 4-1. Sullivan challenged the play for offside, but the call was upheld after a video review.
Guentzel scored on the power play at 9:20 to cut it to 4-2. He has five goals in the past two games and 10 points (seven goals, three assists) during a six-game point streak.
Kopitar scored an empty-net goal at 19:13 to make it 5-2.
Guentzel gave the Penguins a 1-0 lead at 5:30 of the first period with a shorthanded goal, scoring with a backhand on a rebound in the crease after Quick stopped Sidney Crosby on a 2-on-1.
Carter tied it 1-1 at 10:58 with a slap shot from the top of the right circle after stealing the puck from Penguins defenseman Marcus Pettersson at the Kings' blue line.
