Mackenzie MacEachern scored his first NHL goal for St. Louis (21-22-5), which is 0-2-1 in its past three road games. Ryan O'Reilly scored to extend his point streak to five games.
Jordan Binnington made 25 saves but lost in regulation for the first time in his NHL career (4-1-1).
"I thought we played a hard game, competed," Blues coach Craig Berube said. "But we just made too many mistakes that cost us."
LaDue scored his second goal of the season on a wrist shot from the right circle after O'Reilly tied it with a power-play goal at 6:00 of the third period.
"We made it a bit of a common theme to sit back once we got the lead going into the third, so I thought we played well early," said forward Brendan Leipsic, who had two assists for his first multipoint game with the Kings. "They got a power-play goal, but we kept pushing and Paulie made a great shot there and it was enough to hold up."
O'Reilly felt the Blues did not build on the momentum after he scored his 18th goal, which broke a tie with forward David Perron for the team lead.
"I think it gave us a spark, but they responded well too," O'Reilly said. "And they came out and took it to us and got us back on our heels again. We needed a better response after that. After tying it up, we needed some more jump to get going and really take control of the game."
Kopitar gave the Kings a 3-2 lead at 18:16 of the second period.
Doughty tied it 2-2 at 7:15 of the second period during a 5-on-3 power play.
The Blues took a 1-0 lead at 10:31 of the first period when MacEachern scored on a rebound of Vince Dunn's shot. It was MacEachern's first NHL point.
Sundqvist made it 2-0 at 18:49, but Tyler Toffoli responded for the Kings at 19:04 to make it 2-1.
"Maybe not the start we wanted, but we battled back," Kopitar said. "Even that first period, we were down but we generated quite a few chances, just couldn't connect on them. But we stuck with it and at the end of the day, [we] got the job done."
