Claudio Pizarro's early goal proved decisive as the German champions triumphed at New Jersey's Red Bull Arena on Thursday.
Bayern coach Guardiola had anticipated a stiff challenge - Liga MX side Guadalajara having already begun their domestic season - and hailed his team's efforts, which came on the back of victory in last week's Telekom Cup.
"First of all, I would like to say, I'm so, so happy," said the Spaniard, who was once again without the services of several players yet to return to action following Germany's World Cup triumph.
"It's not easy to come here after an eight and a half hour trip, with big jet lag and play against a team like Chivas [Guadalajara], a team I know very well.
"I [have] played two or three times in this [recent] period against them and the last time, I lost 4-1 with Barcelona.
"They [have] already played two or three games in their league. They always play well with the ball. They are so aggressive, they are so dynamic and they make a lot of movement in the 'tiefer' [final third], so I'm very happy with our performance because we have big, big problems with the squad.
"We have a lot of young players, but we competed very well. That's why I am so proud, because I didn't expect to win our last tournament against Borussia Monchengladbach and Wolfsburg and we did it.
"The team played with a good attitude and today [was] the same. I'm so happy."
Bayern's final pre-season fixture, ahead of the DFL-Supercup against Borussia Dortmund on August 13, will see them take on the MLS All-Stars in Portland on Wednesday.
"We'll recover the players who played 90 minutes [or] 80 minutes, and prepare and look forward," added Guardiola.
"We can train [for] one or two or three good sessions, because we need to train in this period, and after we prepare for the last game against the MLS All-Stars.
"I am pretty sure we are going to see a very good game in Portland."
