Perron tied it 2-2 at 9:15 of the second period with a one-timer off a cross-slot pass from Dominik Kubalik.
Danault put Los Angeles back in front 3-2 at 16:18 with his own one-timer, but Perron again tied it 3-3 at 11:14 of the third period with a power-play goal from the left circle.
Kopitar made it 4-3 at 13:16. Husso made the initial save on Kempe, but he didn't realize the puck had slipped out from under his pads, and Kopitar dove to knock it over the line.
"We were never able to get any momentum off our goals," Lalonde said. "There were three times we scored where they seemed to score immediately after, but getting a point after trailing in the third period is a good sign."
Kings defenseman Alexander Edler was a late scratch after being hit in the face with a puck during warmups, and forward Alex Iafallo left with a lower-body injury in the third period.
"Edler didn't play, which is never a good sign, but we'll know more in the morning," McLellan said. "I don't have any update on Iafallo yet."
NOTES: Kings defenseman Sean Walker, who replaced Edler, was plus-2 in 11:41 of ice time. … Red Wings radio analyst Paul Woods called his 3,000th game. The 67-year-old played his entire 501-game NHL career for Detroit between 1977-84.