Los Angeles continued to press and Landon Donovan nearly fired them ahead when he latched onto a long ball over the top from Stefan Ishizaki, but he just could not guide the ball over Frei with a first-time effort.
The Galaxy threatened just before the break when Baggio Husidic laid the ball into the path of Marcelo Sarvas, who struck with venom from the edge of the area, but Frei was able to make the save to deny the midfielder.
In the second half, Seattle responded as DeAndre Yedlin raided down the right and lifted a cross to the back post for Clint Dempsey. The forward headed the ball into the middle of the box, but no Sounders player could take advantage of the loose ball.
The Galaxy went close again as Gyasi Zardes picked up the ball 30 yards from goal and drove towards the box. The striker let fly with a powerful strike that went inches past the post, with Frei beaten.
The Sounders took the lead in the 86th minute when Dempsey picked out the run of Pappa down the left and the midfielder fired the ball past Jaime Penedo into the top corner.
Alan Gordon had a great chance to level the scores late on, but he could only shoot straight at Frei from close range after latching onto a cross into the box.
Pappa sealed the victory as he won the ball from Penedo and chipped into the empty net to secure the MLS Supporters Shield for the Sounders.