Dane Richards and Juan Pablo Angel scored as the Red Bulls (13-8-5) moved into a first-place tie with Columbus in the Eastern Conference with the win over Los Angeles (15-6-5).
Richards gave New York a 1-0 lead in the 36th minute. Joel Lindpere's 11-yard line drive ricocheted off the left post to Richards, who converted from 7 yards.
Angel scored his 13th goal of the season in the 60th minute on a penalty kick after Galaxy defender Yohance Marshall tripped Richards from behind in the penalty area.
Angel trails Los Angeles' Edson Buddle by one goal in the race for the goal-scoring championship.
Beckham, who played the entire game, had his best chance to score in the 66th minute on a 32-yard free kick. But goalkeeper Bouna Coundoul jumped in front of the left post to punch the ball away. Coundoul finished with three saves for his ninth shutout.
Beckham had played twice in the past two weeks as a substitute since tearing his left Achilles' tendon while with AC Milan in March.
Thierry Henry did not make the trip because of a sprained right knee.
Galaxy defender Omar Gonzalez also missed the game with a suspension for accumulating too many yellow cards.