The goal was part of a four-point performance from Kopitar.
Jonathan Quick stopped 20 of Detroit's 21 shots en route to his 28th win of the season, helping the Kings continue a sequence of alternating wins and losses in their past seven games.
The defeat was the eighth in a row (0-7-1) for the Red Wings, who fell to 0-3-0 on their five-game Western swing.
Kopitar put in the tiebreaking goal at 8:22 of the final period, exactly two minutes after he drew an interference penalty on Red Wings center Frans Nielsen.
Drew Doughty and Dustin Brown assisted the goal, which technically was not credited as a power-play marker.
Kopitar's 29 goals are his most since he also tallied 29 in 2014. He had two when the Kings won 4-1 at Detroit in November.
Kings center Tyler Toffoli made it a two-goal difference with 1:30 remaining when he followed in his own shot that had been stopped by Red Wings goalie Jared Coreau. The goal was his 23rd of the season.
Brown completed the scoring 18 seconds later with an empty-netter on a power play. His 21st goal was assisted by Doughty and Kopitar, the third helper of the night for each.
Coreau, playing just his third game this season, fell to 0-2-0. He stopped 18 shots.
Kings defenseman Paul LaDue played a hand in the game's first two goals, one for each team.
LaDue opened the scoring at 8:55 of the first period, assisted by Kopitar and Alex Iafallo. It was the second-year King's third goal of the season.
Despite being out shot 13-11, the Kings retained the 1-0 lead through two periods, but LaDue was called for high-sticking at the 20:00 mark of the second period.
The Red Wings began the third period on a power play, and they quickly took advantage when Gustav Nyquist tied the game just 45 seconds in. The goal was the veteran right winger's second in two games and 18th of the season. Nielsen and Niklas Kronwall were credited with assists on the play.
--Field Level Media
Detroit | Los Angeles | |
Gustav Nyquist 1 | Points | Anze Kopitar 4 |
Gustav Nyquist 1 | Goals | Anze Kopitar 1 |
Niklas Kronwall 1 | Assists | Anze Kopitar 3 |
Gustav Nyquist 1 | Power Play Goals | Dustin Brown 1 |
N/A | Short Handed Goals | N/A |
Jared Coreau .857 | Save Percentage | Jonathan Quick .952 |
Jared Coreau 18 | Saves | Jonathan Quick 20 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Detroit | 21 | 1 | 1-2 | 3-4 | 10 | 24 |
Los Angeles | 22 | 4 | 1-4 | 1-2 | 6 | 23 |