Eliminated from postseason consideration last week, the Union fell to 7-14-7 with two games remaining.
Los Angeles added to its MLS-best point total. The Galaxy (17-6-5) have 56 points.
Beckham, who was replaced in the 76th minute by Jovan Kirovski, was introduced to a Philadelphia tradition - being booed by many of the PPL-record 18,779 in attendance every time he touched the ball.
In the early part of the first half, the Union, as they have so frequently this year, took it to a highly regarded opponent.
Sebastien Le Toux, touted by team manager Peter Nowak as an MVP candidate, sent a bender from 35 yards out that just sailed over the crossbar in the third minute.
In the 12th minute, midfielder Fred suffered a gash in around hisnear an eye. He was replaced a few minutes later by Kyle Nakazawa. Fred's creativity in the midfield was missed.
But Le Toux continued to make dangerous runs. In the 18th minute, after taking a feed from Andrew Jacobson, he sent a pass from the left side inside the box to Danny Mwanga, who was stopped in front of the goal by a sliding keeper Donovan Ricketts.
With the Union applying most of the pressure, the momentum suddenly changed with the simple corner kick by Beckham and Buddle's finishing touch.
Even though Beckham doesn't run his defenders into the ground, often serving as a stationary target, all it took was one strike of the ball on the corner kick for him to have a major impact.
Los Angeles had another good chance late in the first half when Union keeper Brad Knighton bobbled a cross from Chris Birchall, but Galaxy defender Sean Franklin failed to tap it in.
The Union's continued to create second-half scoring chances. In the 73d minute, Le Toux flicked a cross from Jacobson just past the far post.
Moments later, Ricketts made a diving save on a 10-yard shot from an angle on the right side by Shea Salinas.
Knighton made a sensational diving save in the 78th minute on a Landon Donovan breakaway, his most impressive save of an entertaining contest.