Johnson headed down a free kick in the 59th minute to set up Perry Kitchen for the volley finish, and Luis Silva added a third United goal in the 70th minute, his fifth goal in five games.
The victory gave United 34 points, one point behind Sporting Kansas City for the top spot in the Eastern Conference. It also ended at four games a winning streak for Chivas USA.
Erick Torres scored in his sixth consecutive game for Chivas on a penalty kick in the 84th minute, ending Bill Hamid's shutout bid.
Hamid was starting in his 100th game, making him the youngest MLS goalkeeper to reach that milestone.