Birthday boy Vela scored a stunning chip on the stroke of half-time to ensure reigning Supporters' Shield champions LAFC made the perfect start to the 2020 season on Sunday.
Co-owner David Beckham, his famous wife Victoria and Inter's hierarchy were in the stands as the expansion franchise made history in Los Angeles.
Inter battled in their first-ever MLS match but Diego Alonso's side came unstuck following a moment of brilliance from Vela on his 31st birthday.
Former Arsenal forward Vela – who scored a record-breaking 34 goals in a MVP season last term – chipped the ball over Inter captain and goalkeeper Luis Robles in the 44th minute at Banc of California Stadium.
"Surely we have to improve in football, but with this heart and with this intensity with which the team plays, we will surely win many games," said Inter head coach Alonso.
"Against maybe the best team in the league we gave a tremendous picture today of what we can become. With only six weeks of work, the merit is certainly from the footballers for what we have done today and the work they have done."
Trailing to Robert Beric's 46th-minute opener, the Sounders equalized via Morris just past the hour mark before he netted the winner in the third minute of stoppage time.
Elsewhere, Kevin Molino scored twice as Minnesota United upstaged Portland Timbers 3-1, New York Red Bulls edged Cincinnati 3-2 and 10-man New York City lost 1-0 away to Columbus Crew.