Bruce Arena's men, who had already sealed their MLS Cup berth, came within inches of moving ahead inside just four minutes, with Liverpool legend Steven Gerrard watching a free kick cannon off the crossbar.
The hosts finally earned the breakthrough shortly after the half-hour mark, when Keane's first-time volley from outside the box found the top corner to leave Adam Kwarasey with no chance.
Galaxy rested on their laurels and the Timbers started the second period well, before flipping the game on its head midway through the half. First, Adi levelled up on 65 minutes, before converting a penalty three minutes later after being fouled by Dan Gargan in the area.
Diego Chara added a third in the final quarter as the visitors took a big step toward the points, but Keane reduced the arrears with six minutes to play.
However, Darlington Nagbe struck moments later, as did Maximiliano Urruti, as Portland rounded off an emphatic second-half display to move fourth in the Western Conference by three points, with one game to play.
They host bottom-of-the-table Colorado Rapids in Oregon next week.