Each team scored after the end of a scoreless regulation to share the points in a dramatic finish.
Robbie Keane scored the game's first goal goal in stoppage time, surging into the box and heading in Dan Gargan's long throw make it 1-0.
LA was celebrating, but Portland made sure it picked up a point shortly after. A free ball wide of the goalmouth was picked up by Diego Valeri, who went to the the far post to level the match at 1-1.
Portland's record now stands at 1-3-6, while LA moved to 2-2-3.