Drew Doughty scored the game-winner in the 2, at Staples Center.
Justin Williams, Jeff Carter and Anze Kopitar had a goal and an assist apiece while Slava Voynov also scored for the Kings, who earned their second straight win. Jonathan Quick stopped 22 shots.
Jimmy Howard returned from a three-game absence because of a strained groin and allowed four goals on 26 shots.
Los Angeles opened the scoring at the 6:48 mark of the first period when Doughty's wrister from the right point was stopped by Howard, but Williams was there to jam the puck through the goaltender's pads and across the goal line.
Then, with 6:45 left in the opening frame, Los Angeles added to its lead while shorthanded. After Kopitar grabbed an errant pass at his blue line and raced down the right side of the ice, he fired a wrister from the right circle that sailed into the far side of the net to make it a 2-0 game after one.
The Red Wings cut their deficit in half 4:06 into the second when Henrik Zetterberg fired a cross-ice pass to Hudler at the right circle, where he stopped the puck with his skate and kicked it to his stick before firing a hard wrister through the short side.
But the Kings regained their two-goal cushion just past the midpoint of the middle stanza when Doughty's shot from the high slot deflected off Detroit's Ian White in the slot and bounced past Howard.
The lead stretched to 4-1 at the 8:23 mark of the third while on the power play after Jarret Stoll sent a pass from the left corner through a crowd to the right of the net, where Voynov banked a shot in off the right pad of Howard as he went down to make the save.
Franzen cleaned up a rebound off a Brad Stuart slap shot from the right point with 6:30 left in the game to bring the Red Wings back within two, but Carter's empty-net goal within the final minute sealed the outcome.
Kings forward Dustin Brown had two assists to extend his points streak to nine games, tying his career high. He has five goals and nine assists in the streak...Detroit took the season series, 3-1...Howard fell to 9-3-0 against the Pacific Division this season...Los Angeles went 1-for-2 on the power play, while Detroit went scoreless in four power-play opportunities.