Omar Gonzalez and Mike Magee scored on headers for the Galaxy (13-3-9), who moved six points ahead of last year's MLS Cup runner-ups in the Western Conference.
Beckham is tied for the league lead with 10 assists this season.
''It's nice to set up goals,'' Beckham said. ''But it's more important that we are six points clear. That's what we aimed to do.''
Marvin Chavez scored in the 9th minute for Dallas (12-6-6), his fourth goal in the past three games.
Dallas, which beat the Galaxy 2-1 in the season's first meeting on May 1, was unbeaten in its last four games. This was another rematch of last year's conference finals, which saw Dallas prevail 3-0.
''It's always fun playing them,'' Dallas defender George John said. ''They're a great side. The best team in the league right now.''
The Galaxy grabbed the lead for good when Beckham sent in a cross from the sideline. Gregg Berhalter got a head on it, pushing the ball back out of the box toward Juninho.
The Brazilian midfielder's low shot hit the left post and went in for a 2-1 lead.
The Galaxy added an insurance goal in the 81st minute when Magee converted Beckham's corner kick as the Galaxy got back in the win column after their 14-game unbeaten streak was snapped by Portland on Wednesday.
''Tonight was about showing character,'' Beckham said. ''It was up to us to prove that that was not us, that's not the way we play.''
Chavez put Dallas ahead when he received a pass from Maicon Santos and unleashed a strike from outside the box that rattled off the crossbar and left post before going in.
But the Galaxy evened things at 1-1 in the 32nd on some miscommunication by Dallas. Beckham's deep cross forced goalkeeper Kevin Hartman to collide mid-air with his own defender, allowing the ball to land gently in the box after a slight deflection.
Gonzalez, wearing a face shield to protect his fractured nose, took the ball off a big hop and headed it home.
''I felt like I was striking the ball well tonight,'' Beckham said. ''I felt every ball I played was in the right place.''
Despite a rare subpar performance, Hartman entered the MLS record books.
In playing his 378th career game, Hartman tied Steve Ralston for MLS' all-time record. Hartman, the MLS Player of the Month for July, also matched Ralston's mark of games started with 372.