Christian Ramirez opened the scoring in the 28th minute for Los Angeles (12-2-4) by sending a free kick under the wall and past a diving Tim Melia. Rossi made it 2-0 in the 50th by curling a shot from the 18-yard line and Vela scored from the penalty spot in the 63rd for a 3-0 lead.
Rodolfo Zelaya scored on a breakaway in the 89th for a 4-1 lead and Mohamed El-Munir finished an individual effort two minutes later.
Kansas City (4-7-7) dropped its second straight following a three-game undefeated run. Yohan Croizet scored for Kansas City in the 85th after settling Ilie Sanchez's chipped pass and finishing with his left foot.