It was the fourth win in the last five games for the Galaxy (17-6-5), who lead MLS with 56 points.
In the 27th minute, Beckham lofted a perfect corner kick for Buddle, who headed the ball past goalkeeper Brad Knighton.
Before the corner kick, a large group of Union supporters were booing Beckham. Following the goal, Beckham smiled and clapped his hands toward the crowd.
This was just the fifth game this season for Beckham, who has been recovering from a torn left Achilles' tendon injury.
Despite a PPL Park-record crowd of 18,779, the Union struggled and had just one shot in the first half.