Los Angeles (3-2-2) won its second straight game, while Sporting KC (2-2-3) had its four-game undefeated streak snapped.
Gonzalez redirected Juninho's corner kick with his right shin in the fourth minute of extra time and it deflected off a defender's knee into the back of the net.
Krisztian Nemeth tied it in the 22nd minute for Sporting KC. Dominic Dwyer ran down a deep ball in the corner and drew three defenders when he dribbled into the 18-yard box. He found Benny Feilhaber at the penalty spot, who one-touched it to Nemeth for the finish.
Gyasi Zardes, who played in the U.S. national team's exhibition game against Mexico on Wednesday night, entered the match in the 69th minute.