Adam Erne opened the scoring to put Detroit ahead, 1-0, early in the first period, but Los Angeles found the back of the net twice and led, 2-1, after 20 minutes.
Perron evened the score, 2-2, halfway through the second period, then made it a 3-3 game with a power-play goal in the third. The Kings had a 4-3 lead with 90 seconds left in the final frame and had an opportunity to capitalize on an empty Red Wings net, but captain Dylan Larkin made a diving play to keep Detroit's comeback hopes alive.
"It was an amazing play," Red Wings head coach Derek Lalonde said. "He never gave up on it. It's a good message for everybody."
Oskar Sundqvist's goal with 41 seconds left in regulation sent the game into overtime, but Los Angeles netted the game-winner at 1:12 in the extra frame.
Ville Husso made 31 saves in the loss for Detroit (2-0-1; 5 points), which finished 4-for-4 on the penalty kill against the Kings.
Filip Zadina logged 14:25 of ice time in his season debut, slotting in for Tyler Bertuzzi (upper body), who Lalonde announced after Monday's morning skate will be out for 4-6 weeks.
NEXT UP: The Red Wings will face the Chicago Blackhawks on Friday night at the United Center. Puck drop is set for 8:30 p.m. ET/7:30 p.m. CT.