Mora scored the equalizer unassisted in the 76th minute. It was his fifth goal this season.
Portland (11-11-10), which scored multiple goals in a club-record four straight wins entering play, jumped out to a 1-0 lead in the 5th minute when Santiago Moreno used an assist from Dairon Asprilla to score his third goal of the season.
The Timbers regained the lead on an own-goal by Zavaleta in the 38th minute. But Costa used an assist from Raheem Edwards in the 43rd minute to net his first goal of the season and Zavaleta scored again — in the first minute of stoppage time — to give the Galaxy a 3-2 lead at halftime.
David Bingham finished with two saves for the Timbers. Jonathan Bond stopped two shots for the Galaxy.
Portland has collected a league-high 17 points since Miles Joseph took over as interim manager in late August.
The Galaxy improved to 3-0-3 in their last six meetings with the Timbers in all competitions. It is the longest unbeaten run for either team in the series.
AP soccer: https://apnews.com/hub/soccer
The Associated Press