Jurgen Klopp's side made light work of the Hammers at Anfield to move above Chelsea at the top of the table, the latter having beaten Huddersfield Town 3-0 in their opener.
Liverpool handed full debuts to new signings Alisson and Naby Keita, the latter producing a hugely impressive performance at the heart of midfield, while Xherdan Shaqiri made a late appearance off the bench.
But it was two of the Reds' established heroes who sealed the three points, Salah prodding home Andy Robertson's 19th-minute cross before Mane netted twice from inside the box either side of half-time. Substitute Daniel Sturridge bundled in a late fourth.
Mane's second should have been disallowed for offside but that was the only complaint West Ham could have about the result, with Manuel Pellegrini's expensively-assembled side looking a long way from settled.
Liverpool, though, was comfortable without ever needing to hit top gear and certainly looks like the title challenger most consider it to be this season.
Liverpool now has a full eight days to recover until its second league game of the season against Crystal Palace on 21 August (NZST).
West Ham, however, is back in action next Sunday (NZST) when Bournemouth visits London Stadium.