The Galaxy (18-7-5) will face Seattle in the playoffs after winning the Supporters' Shield for finishing with the league's best record.
"Tonight was a step forward," Galaxy coach Bruce Arena said. "We haven't been in a game where we've been forced to show up, play hard, fight and scrap for everything we could get. We did that tonight."
The Supporters' Shield is the first trophy that the Galaxy won since Beckham joined the team in 2007.
"I've won quite a few accolades and awards over the years," Beckham said. "But for us, it's not over. We want to go all the way and we want to win everything."
"I think any of those four teams could end up in the championship game," Dallas coach Schellas Hyndman said. "We would have won the Supporter's Shield last year with the points we have. That's just a compliment to all the other teams that are doing so well."
Juninho broke a 1-1 tie in the 46th minute. Dallas defender Zach Loyd headed Landon Donovan's aerial pass to Juninho, who volleyed it into the net from 18 yards.
Harris gave Dallas a 1-0 lead in the 22nd minute with a 5-yard header off Eric Alexander's left-wing cross. Alexander began the play by intercepting Galaxy defender Sean Franklin's attempted clearance.
"To my surprise, they came out with all their guns," Arena said. "We had to keep our concentration for 90 minutes."
Beckham tied it in the 33rd minute. Donovan pushed Dallas' Jackson Goncalves away to steal the ball near the left end line and passed to Beckham, who fired a low 23-yard shot between goalkeeper Dario Sala and the left post.
Donovan received his league-leading 16th assist, a career high.
Edson Buddle had two chances to tie San Jose's Chris Wondolowski for the league lead goals. But in the 67th minute, Sala used his right hand to block Buddle's 7-yard header off Beckham's corner kick.
In the 68th minute, Sala dropped Beckham's corner kick but Buddle shot the loose ball wide of the right post.
Wondolowski finished with 18 goals.