Cleveland, making his first MLS appearance since 2018 in place of the injured Stefan Frei, made three saves for the league-leading Sounders, who have outscored their opponents 13-2 this season.
Frei, who missed just his sixth league match since joining Seattle in 2014, suffered a sprained left knee Wednesday in a 1-0 victory at San Jose and is expected to miss at least a month.
Los Angeles saw its winless streak extended to four matches.
Arreaga scored his first career MLS goal off a corner kick from Joao Paulo in the 57th minute. Arreaga flicked on a header from the near post, and it found its way past diving LAFC goalkeeper Pablo Sisniega and into the far side netting.
Los Angeles' Carlos Vela, the 2019 MVP when he scored a league-record 34 goals, came on as a substitute in the 70th minute. It was Vela's first appearance since he left the season opener 22 minutes in with a quadriceps injury.
But even Vela's presence didn't help, as the Sounders made it 2-0 on a counterattack in the 73rd minute. Alex Roldan's cross from the right wing found Smith at the top of the six-yard box, and he put a forceful header into the net.
The first half was scoreless, despite Los Angeles controlling possession for much of the time. LAFC struggled to finish in the final third against Seattle's five-man backline and put just one shot on goal.
The Sounders finally got untracked late in the first half and had the best scoring opportunity of the opening 45 minutes when Cristian Roldan found Smith just inside the top of the 18-yard box on a two-on-one break. But Smith sliced his 15-yard shot wide of the left post.