Jordan Morris and Fredy Montero also scored for the Sounders (1-2-0), who had lost their first two games of the regular season by 1-0 margins.
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Javier "Chicharito" Hernandez and Douglas Costa scored for Los Angeles (2-1-0), which hadn't conceded a goal in its first two matches.
The Sounders, who have an eight-game unbeaten streak against the Galaxy (5-0-3) and have lost just once in the past 15 meetings against their Western Conference rivals (8-1-6), scored on a corner kick, penalty kick and free kick.
Arreaga's winner came on Alex Roldan's free kick from about 30 yards out on the right wing. He found an unmarked Arreaga just outside the middle of the six-yard box, and Arreaga put a header into the upper left corner of the net.
The Galaxy opened the scoring in the sixth minute. Raheem Edwards played a ball into the area for Rayan Raveloson, who fed "Chicharito" for a left-footed blast from just outside the top of the six-yard box that soared over goalkeeper Stefan Frei and just under the crossbar.
Morris tied it in the 17th minute on a corner kick by Joao Paulo. Cristian Roldan flicked a header that went off the leg of a Galaxy defender and deflected to a wide-open Morris in front of the net. He fell while reaching his leg back to control the ball, but was able to swing his leg forward while on the ground to roll the ball just past goalie Jonathan Bond and over the goal line.
It was Morris' first MLS goal since 2020 after missing nearly all of last season with a knee injury.
Seattle took a 2-1 lead in first-half stoppage time after Montero was taken down in the far left corner of the penalty area by Julian Araujo. Montero converted the penalty kick, putting his shot into the lower left corner of the net as Bond guessed the other way.
The Galaxy tied the score at 2-2 in the 48th minute on a free kick from just outside the top right of the penalty area by Costa. His left-footed kick went off the wall of Seattle defenders and deflected into the far lower corner of the net, leaving Frei no chance.
Xavier Arreaga's header propels Sounders to victory
The Seattle Sounders take the 3-2 win over the LA Galaxy thanks to a goal by Xavier Arreaga.
Douglas Costa scores to tie it in 48th minute
Douglas Costa scores in the 48th minute as the LA Galaxy ties it up evenly at 2 with the Seattle Sounders.
Jordan Morris equalizes for Seattle during goalmouth scramble
The Seattle Sounders draw level with the LA Galaxy after Jordan Morris somehow pokes it in from close range.