John got the game's only goal when he tallied on the rebound after a header by Eric Hassli banged off the crossbar as the Galaxy were playing a man down due to red card issued to Leornado.
John's goal came after Los Angeles goalkeeper Carlo Cudicini denied Kenny Cooper on a penalty kick in the 60th minute.
The win boosted Dallas to a 5-1-1 mark, good for 16 points.
Landon Donovan also was stopped on a second-half penalty kick for the Galaxy (2-1-2), who fell for the first time this year.
Celebrity Families of 2014 [PHOTOS]