Goals either side of the break from Argentine striker Ismael Sosa, who only joined UNAM from Universidad Catolica in December, gave the home side the ascendency at the Estadio Olimpico Universario in Mexico City.
Galaxy's rookie defender Kyle Venter responded by pulling one back for the visitors late in the match.
LA head coach Bruce Arena suggested it was a good experience for his side as they continue to prepare for the upcoming 2014 MLS season.
"I think that it was a good exercise for our team," said Arena.
"Obviously, the altitude was very challenging, but Pumas has a good team and this was a good training exercise."
The Galaxy play their next preseason match on Saturday in Fresno when they take on the San Jose Earthquakes for the Central California Cup.
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball