Striker Alan Gordon opened the scoring in the 50th minute, chesting down a pinpoint through ball from Landon Donovan and blasting the ball into the back of the net with his right foot.
Pachuca, winners of this year's CONCACAF Champions' Cup, equalised in the 78th when substitute Damian Alvarez crossed from the right for striker Rafael Marquez Lugo to slide the ball past goalkeeper Joe Cannon.
The Galaxy, outplayed for most of the first half in front of 19,317 fans at the Home Depot Center, regained the lead just three minutes later.
Substitute Cobi Jones, given space on the left by U.S. international Donovan, danced round two defenders before unleashing a right-footed shot that Donovan deflected into the net.
Pachuca, who became the first Mexican team to win the Copa Sudamericana last year, dominated the opening half but were repeatedly thwarted by Cannon.
Pushing forward at every opportunity, Pachuca came close to scoring in the sixth minute when midfielder Andres Chitiva set up Luis Gabriel Rey with a superb pass that split the Galaxy defence.
Although striker Rey had space and time, his powerful right-foot shot was tipped over the bar by Cannon.
Under continual pressure from the Pachuca attack, Cannon pulled off another good save in the 16th minute when he got his right foot to Lugo's shot after the striker had been put through by Christian Gimenez.
England midfielder Beckham, as had been widely expected, was ruled out of the match to give him more time to shake off a lingering ankle injury.
The SuperLiga, which offers $1 million (485,000 pounds) to the champions, is a regional competition featuring four Major League Soccer sides from the U.S. and teams from the Mexican first division.
A knockout phase will follow the group stage with the final scheduled for August 29 at a venue yet to be decided.