Meanwhile, in the other group game, Senegalese striker Dame Ndoye's first-half goal proved the difference as FC Copenhagen recorded their opening victory with a 1-0 win over Sparta Prague.
Beckham, who left Spanish giants Real Madrid for Major League Soccer in the United States in 2007, scored for the Galaxy in the 2-1 win over FC Dallas on Sunday that earned the club the Supporters' Shield for Major Soccer League's top point-scoring team.
The world's most expensive player returned in Wednesday night's 1-0 Champions League win over FC Zurich, coming on as a second-half substitute after two months out with ankle problems.
In Group K , unbeaten PSV Eindhoven went three points clear at the top with a 1-0 win at home to Denmark's FC Copenhagen, as Jonathan Reis made up for having his first-half penalty saved by Johan Wiland when he fired in a 72nd-minute decider.
The Crawley FC team left the Broadfield Stadium on Thursday afternoon following a press conference at which manager Steve Evans predicted a 1-0 win for Crawley.