Beckham scored with two of his trademark long, curving kicks in the first half after the Galaxy had fallen behind, 2-0.
He nearly had a third goal but was upended by a defender before he could get off a shot into an open net early in the second half.
Fabian Espindola and Kenny Deuchar scored early in the first half for Real Salt Lake and Nick Rimando finished with four saves, including a diving stop on a point-blank header by MLS leading scorer Landon Donovan
Galaxy goalkeeper Steve Cronin also knocked away some tough shots to preserve the tie and finished with five saves.
Beckham got the Galaxy to within 2-1 with one of his trademark benders from about 25 yards in the 36th minute. He almost one-timed it, but instead controlled it and reared back for a kick that curved around the defense and past Rimando inside the far post.
Beckham did it again in the 40th minute. Salt Lake's Dema Kovalenko was called for a foul and the Galaxy was awarded a free kick from 29 yards in the middle of the field.
Beckham wasn't the one who was fouled, but there was no doubt he would be taking the free kick. The home fans went silent as he blasted a shot that went over the wall of Salt Lake players and curved inside the left post again as Rimando dived helplessly for it.
The crowd of 25,500 was the third-largest in team history.