Josh Wolff and Davy Arnaud scored two minutes apart in the second half to bring victory for Kansas City.
Both sides came into the match sharing last place in their respective conferences and six points out of playoff contention, the Wizards winless in their last four and the Galaxy winless in their last 11, a club record.
The Wizards lineup took a new look with recent acquisitions Herculez Gomez and Abe Thompson starting and Claudio Lopez having a seat on the reserves' bench for the first time all season. The Galaxy were fortified with the return of Beckham and U.S. internationals Landon Donovan and Eddie Lewis.
The match began evenly as the sides probed all parts of the field looking for an opening. Forwards Edson Buddle and Landon Donovan of the Galaxy took the first shots of the match in the ninth and 12th minutes but Wizards goalkeeper Kevin Hartman was not troubled.
Arnaud, playing attacking midfield for the first time all season, provided initiative for K.C. as his forays nearly loosed frontrunners Wolff and Thompson on different occasions and wide midfielders Gomez and Roger Espinoza who pushed high on the outside.
Action in the penalty areas increased in the last 15 minutes of the first half through an increase in direct play and more physicality. In the 41st minute, Donovan was fouled 29 yards out and a bit to the left of goal. Beckham stepped up for the free kick, but his attempt sailed well over the bar.
The last 10 minutes featured the strongest chances of the first half as the Galaxy threatened again in the 43rd minute when Donovan chested down for Buddle at the top of the Wizards box, but the 27-year-old floated his attempt high. Kansas City countered in the next two minutes through Thompson who received a pass from Wolff eight yards out and shot into the gut of L.A. netminder Josh Wicks.
Wicks then gave up a long rebound of a Jack Jewsbury blast from 24 yards. On the doorstep was Thompson, but he was foiled by Galaxy defender Troy Roberts, who safely cleared.
Beckham nearly broke open the match 10 minutes into the second half with a 25-yard blast from the middle that swerved to the left of Hartman's goal. The willingness to fire signaled an increase in attack that promised to show results soon.
The 67th minute produced. Gomez sent in another blistering cross from the right wing, this time for Wolff who pulled the ball with the sole of his right boot while twisting away from his defender. The ball rolled quickly past a floundering Wicks and hit the back of the net at the far post. The goal was Wolff's second of the season after rejoining the Wizards in July from 1860 Munich.
The match now turned another gear, and it was Kansas City who pushed it further with a second goal just two minutes later. With space and time just off center 33 yards out, Arnaud drove for Wicks' left post and found it with a powerful drive that bolted into the upper corner. Kansas City could now see the light in their playoff hopes that three points would bring them.
As the Galaxy picked up possession in the latter part of the match, the Wizards held strong and countered when possible, a formula that allowed them to see out the match and look to next week where they could take their next step in their effort to make the postseason.
The Wizards will play host to Toronto FC next week in the next game that will loom large while the Galaxy will entertain D.C. United with their playoff hopes dwindling.
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