It was the Galaxy's first victory since Beckham joined his new team.
The inaugural SuperLiga involves four Major League Soccer teams and four from the Mexican first division in a round-robin tournament.
Beckham was again missing with an ankle injury and his absence gave the club a reminder of life pre-Beckham. There were plenty of empty seats in the 27,000-seat stadium and a lack of camera flashes. The announced attendance was 19,317.
The Galaxy winner came in the 81st minute when a Donovan converted a Cobi Jones pass.
The Galaxy's next SuperLiga game is against Chivas Guadalajara on Saturday, when Pachuca will visit Dallas.