Dallas will now meet the Colorado Rapids in Sunday's final in Toronto with the MLS championship at stake and both team seeking their first league title.
Beckham looked short of full fitness as the Galaxy were out-thought by an intelligent and better-organised Dallas team.
Colombian midfielder David Ferreira put Dallas in front in the 26th minute when he was allowed to turn and shoot on the edge of the area and fired into the bottom corner.
The goal came against the run of play with Dallas keeper Kevin Hartman having been busy to keep out efforts from Juninho and Mike Magee and a bouncing free-kick from Beckham.
Former Galaxy keeper Hartman then tipped a good effort from Landon Donovan wide but Dallas took a firm grip on the game in the 54th minute when, after a smart break, Brek Shea slipped a low ball across the box which George John converted at the back post.
There was more woeful defending from the Galaxy when Dallas added their third, the classy Ferreira linking up with Marvin Chavez who confidently slotted home.
"Kevin made three or four unbelievable saves early, we couldn't beat him tonight," said Donovan.
"They made three or four good plays. We fell asleep on one play and (Ferreira) the best player in the league this season made us pay for it," he added.
Dallas, founder members of the league in 1996, will be playing in their first league final.
