After being frustrated by Impact goalie Donovan Ricketts, who finished with six saves, the Galaxy drew even on a trademark free kick goal from Beckham, who found the top right corner of the net on the shot from the right side.
Los Angeles improved to 3-5-2 with the draw, breaking a two-game losing streak.
Ricketts preserved the tie for Montreal (3-5-3) in stoppage time when he punched away a volley from Marcelo Sarvas.
Davy Arnaud scored on an assist from Nelson Rivas in the 8th minute for the Impact.
Celebrity Breakups and divorces of 2014 [PHOTOS]