Sporting is the first club to begin a season with five wins since Los Angeles opened 12-0 in 1996, Major League Soccer's inaugural year. Kansas City also extended its home unbeaten streak to five matches against Los Angeles, which is 1-3 after winning the MLS Cup last season.
Kansas City has four shutouts in five matches, and goalkeeper Jimmy Nielsen did not have to make a save against the Galaxy.
Beckham has been plagued by a series of nagging injuries and didn't make the trip. Landon Donovan returned from a quadriceps injury that kept him out of Los Angeles' 3-1 home loss to New England.
Kamara scored his third goal of the season, connecting in the 40th minute off Bobby Convey's first assist with his new team. Kamara beat right back Sean Franklin to Convey's cross at the edge of the 6-yard box and curled the ball inside the far post.