Alan Pulido, Luis Martins and Daniel Salloi all scored within 16 minutes as KC raced to a 3-0 lead. Salloi's classy volley took his tally to nine goals this MLS season.
Israeli midfielder Gadi Kinda added a fourth in the 58th minute with Graham Zusi getting his second assist, before LAFC got a consolation from Danny Musovski.
The win lifted Sporting KC past Seattle Sounders who conceded in the 90th minute to draw 1-1 at home with Dallas.
Fredy Montero had put the Sounders ahead in the 72nd minute with a set-piece header but Dallas equalised from Franco Jara's 90th-minute close-range strike.
Sporting KC is ahead of Seattle on goal difference, with both sides having 33 points, although the leaders have a game in hand.
LA Galaxy is third after a 1-0 victory over Real Salt Lake, secured by Efrain Alvarez's cool 53rd-minute winner.
Eastern Conference leader New England extended its unbeaten run to five games with a 0-0 draw against Nashville, which slipped to fourth despite the result.
The draw also extends Nashville's undefeated streak to nine games.
Former England international Kieran Gibbs netted a 66th-minute equaliser to earn Inter Miami a 1-1 draw away to fellow Florida outfit Orlando City. The goal was Gibbs's first in the MLS.
Philadelphia Union ended its three-game winless run with a 3-0 victory over Toronto after three first-half strikes.
Ola Kamara and Yordy Reyna both netted doubles as DC United won 4-2 over Columbus Crew.
Tomas Pochettino scored a first-half brace as struggling Austin won 3-2 over Houston Dynamo.
Chicago Fire and 10-man New York City played out a goalless draw, while New York Red Bulls and Cincinnati also ended 0-0 and Portland Timbers drew 1-1 with San Jose Earthquakes.