A stunning free-kick from Dominik Szoboszlai has given Liverpool a 1-nil win against title rivals Arsenal.
The champions are back on top of the early table with a 100 percent record so far.
Aston Villa remain winless from their three top-flight games after going down 3-nil at home to Crystal Palace.
West Ham got a much-needed 3-nil victory at Nottingham Forest for under-pressure manager Graham Potter.
Manchester City suffered back-to-back defeats as they lost 2-1 at Brighton.