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Mohamed Salah completed his hat-trick with a late penalty as Premier League champions Liverpool saw off Leeds on their long-awaited return.
Marcelo Bielsa's side, back in the top flight after 16 years, were impressive throughout and came from behind to level on three occasions.
But Salah - who scored two spot-kicks - had the last word to ensure Jurgen Klopp's team start with a win.
Jack Harrison, Patrick Bamford and Mateusz Klich all scored for Leeds.
Meanwhile Crystal Palace made a winning start to the 2020-21 Premier League season as a volley by Wilfried Zaha proved enough to sink Southampton.
The Ivory Coast forward, who has repeatedly been linked with a move away from Selhurst Park, was unmarked when he produced a clinical finish from Andros Townsend's impressive cross.
Nathan Redmond wasted a great chance following a slick Southampton move, while Palace keeper Vicente Guaita produced an excellent save to keep out a volley by Che Adams.
Guaita then produced a reflex save to deny Danny Ings a last-gasp equaliser.
Premier League Results:
Fulham 0-3 Arsenal.
Crystal Palace 1-0 Southampton.
Liverpool 4-3 Leeds United.