Anthony Mantha and Dylan Larkin each scored on the power play for Detroit, which lost its first two games (0-1-1) for the second time in the past three seasons. Dennis Cholowski got his first two NHL assists, and Bernier made 21 saves.
After Larkin pulled the Red Wings back to 3-2 at 16:00 of the third period, Iafallo scored an empty-net goal with 21 seconds left in the third to put Los Angeles ahead 4-2. It was Iafallo's second multigoal NHL game.
"I think we gave it our best tonight," Red Wings forward Frans Nielsen said. "It was tough, but it was good to see that we can play like that. And if we keep repeating and play the way we did today we're going to win a lot of games."
LaDue gave the Kings a 2-1 lead at 16:14 of the second, scoring his fourth goal in 35 NHL games.
Kopitar put the Kings in front 1-0 at 4:21 of the second, with Kovalchuk getting his 400th assist, but Mantha tied it 1-1 at 8:45 with the 13th power-play goal of his NHL career.
Red Wings defenseman Trevor Daley sustained an upper-body injury in the first period. Daley fell after losing his balance making a pass at the red line and accidentally was hit in the head by Kings rookie Jaret Anderson-Dolan's knee. Red Wings coach Jeff Blashill said Daley will not play at the Anaheim Ducks on Monday, with Joe Hicketts taking his place.
Detroit played the final 51:54 with five defensemen, with Cholowski, Filip Hronek and Libor Sulak each appearing in his second NHL game and Nick Jensen playing 22:51.