Legwand and Shea Weber scored power-play goals in the first period, Eric Nystrom also scored, and Patric Hornqvist had three assists. Carter Hutton made 35 saves in his fourth straight start since Pekka Rinne went on the injured list because of an infection in his surgically repaired hip.
Centre Jeff Carter, who had a hat trick against Nashville the last time the Predators visited Los Angeles on March 4, was placed on the injured list Saturday with a lower-body injury sustained in Wednesday's overtime victory against San Jose.
Trailing 3-1 after two periods despite outshooting Nashville 24-11, the Kings got closer at 9:41 of the third when Brown threw the puck toward the net from the left boards, and it found its way inside the post.
Richards tied it for the Kings on the rebound of a wrist shot by Tyler during a power play at 11:18, but Legwand restored the Predators' lead for good.
Los Angeles outshot Nashville 14-6 in the first, but trailed 2-1 after the Predators connected on their two power plays of the period.
Rich Clune, claimed off waivers from the Kings last January, received a misconduct for instigating a fight with Daniel Carcillo at 7:28 of the period after Carcillo's hard open-ice hit against defenceman Roman Josi. It was Josi's second game back after missing 10 with a concussion.
Carcillo received an additional penalty for kneeing, so the teams continued skating 5-on-5 until about 3 minutes later when Kings defenceman Slava Voynov was sent off for tripping Nystrom. The Predators capitalized on the ensuing power play as Legwand sent a wrist shot from the slot past the screened Quick.
The Kings closed within 2-1 just 16 seconds later when Kopitar put in a rebound of Jake Muzzin's long wrist shot.
Nashville restored its two-goal lead 8:41 into the second period.
Los Angeles defenceman Drew Doughty had the puck in the left corner and tried a backhanded clearing pass around the boards, but the puck struck referee Mike Hasenfratz. Hornqvist then set up Nystrom in front of the net.
NOTES: Los Angeles C Jarret Stoll, who won all five faceoffs he took in the first period, played only a minute in the second period before leaving with an undisclosed injury. ... Los Angeles C Tyler Toffoli and RW Linden Vey were called up from Manchester (AHL). D Keaton Ellerby was claimed off waivers by Winnipeg. ... Nashville C Matt Hendricks missed the game because of an upper-body injury sustained in a collision with Phoenix's Derek Morris on Thursday. ... Los Angeles and Nashville began the day as the top two NHL teams in faceoff percentage, with the Kings winning 55.9 per cent and the Predators winning 55.7 per cent. ... The Kings broke a franchise record with their 76th consecutive sellout — including post-season. The old mark occurred during the early 1990s, when Wayne Gretzky played for them.