Raul Ruidiaz scored at the 11-minute mark before being replaced because of a heel contusion at halftime for the defending MLS Cup champion Sounders, who moved into second place in the Western Conference, two points behind Sporting Kansas City.
Diego Rossi scored for LAFC at 60 minutes, which suffered its second consecutive defeat since resuming play following the MLS is Back Tournament.
LAFC, last year's Supporters' Shield winners, defeated Seattle 4-1 in the MLS tourney's Round of 16, avenging a loss in last year's conference final in Los Angeles.
But the Sounders built a three-goal lead Sunday as Morris scored in the 48th and 49th minutes.
The first of Morris' goals came as midfielder Nicolas Lodeiro made a pass from midfield that sent Morris on a breakaway past two defenders. Morris dribbled around hard-charging LAFC goalkeeper Kenneth Vermeer about 25 yards off his line and rolled the ball into an open net from just inside the top of the 18-yard box.
After the ensuing kickoff, Sounders midfielder Joao Paulo made a run down the right wing and sent a cross to Morris at the top of the 6-yard box near the far post. Morris' half-volley put Seattle up 3-0.
Rossi scored when he took a cross from Jose Cifuentes on a two-on-one break and put a one-timer just past diving Sounders goalkeeper Stefan Frei and inside the left post. Bradley Wright-Phillips also got an assist on the play.
Ruidiaz opened the scoring after LAFC had dominated the early going. A long lead pass from near midfield pinballed off a defender and dropped to Ruidiaz, whose left-footed shot from 30 yards left Vermeer flat-footed and found the upper left corner of the net.