He doubled the advantage with his sixth goal of the season 13 minutes later, converting a through ball from Ned Grabavoy with low shot past the Goats' goalkeeper.
Will Johnson also found the net for Real (10-3-2), which maintained its MLS-best record.
Chivas (4-7-3), meanwhile, lost for the sixth time in eight home games.
McPhee, Cokas 'working on their marriage' after affair
Beautician charged with giving client fatal silicone butt injection