Daniel Salloi and Diego Rubio each scored in the first half to lead
Kansas City (12-6-11), which won the U.S. Open Cup on Wednesday, extended its club-record home unbeaten streak to 24 games.
The Galaxy (7-17-6) haven't won an away game in the series since 2007.
Salloi opened the scoring in the 18th minute on a redirection of Rubio's cross.
Rubio made it 2-0 in the 35th minute. Seth Sinovic ran past the defense for a through ball and crossed it to a wide open Rubio for an easy finish.
Romain Alessandrini bent in a free kick in the 58th minute for Los Angeles. It was the first time this season Sporting KC allowed a goal directly from a free kick.