The Galaxy had the chance to take the lead in the 11th minute when Juninho played a ball over the top of the Portland defence for Robbie Keane to chase. The striker raced into the box but saw his effort well saved by Donovan Ricketts.
The home side continued to press early on and this time only the woodwork prevented them from going ahead as Marcelo Sarvas's shot from 20 yards out rattled the post.
In the second half, Los Angeles threatened again as they produced a good move down the right, which ended as Landon Donovan teed up Keane, but his left-footed volley went just over the bar.
The Galaxy finally took the lead in the 65th minute when Sarvas picked up the ball on the edge of the area and placed a right-footed shot beyond the reach of Ricketts into the net.
Portland took the lead minutes later when Jorge Villfana got behind the Galaxy defence and laid the ball to Valeri whose shot was blocked, but Villafana latched on to the rebound and drove it home.
The home side rallied and had the chance to draw level as they won a free kick on the edge of the penalty area. However, Juninho's well-struck effort was saved by Ricketts, who turned the ball over the bar.
Los Angeles continued to pressure the Portland goal to get their equaliser and they managed to salvage a point when Rauwshan McKenzie put the ball through his own net with four minutes to play.