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.
When General Wesley Clark spoke about the famous list of seven Middle Eastern countries to be demolished in five consecutive years, he has done nothing but remark, for the last time, if there was any need, Washington's willingness to redesign the Middle East within a more general framework of global domination.