With the victory, the Galaxy raised their record to 18-7-5 to win the Supporters' Shield, indicative of the MLS' best regular-season record. Their 59 points gave them sole possession of the top spot in the league-wide standings, edging Real Salt Lake by three points.
After spotting Dallas a 1-0 lead on a header by Atiba Harris in the first half, Los Angeles answered at the 33-minute mark when Landon Donovan entered the penalty area unguarded and found Beckham, who launched a 22-footer into the net.
Juninho got the game-winner in the 46th minute on a shot from the top of the area.
The Galaxy will open the playoffs against Seattle while FC Dallas (12-4-14) will take on Real Salt Lake.