It was the Cherries’ fifth defeat in their last six Premier League matches as they were outclassed by Jurgen Klopp’s team, who warmed up for their crunch Champions League match against Napoli in style.
Bournemouth, without Callum Wilson due to a hamstring injury, were on the back foot from the first whistle and Xherdan Shaqiri had an early free-kick blocked before Salah sliced a shot wide.
David Brooks had the Cherries’ first effort on goal in the 24th minute, but Alisson saved the former Sheffield United star’s eight-yard shot.
The visitors deservedly moved ahead two minutes later when Salah turned home the rebound after Asmir Begovic had spilled Roberto Firmino’s shot, but the Egypt international appeared to be offside.
Bournemouth, who also lost 4-0 in the corresponding fixture last season, had a good chance to equalise nine minutes before half-time, but Nathan Ake completely missed his attempted volley after Virgil van Dijk had failed to clear the danger.
It proved to be a costly miss as Liverpool doubled their advantage soon after the restart, with Salah holding off Steve Cook’s robust challenge before slotting a shot past Begovic into the corner of the net.
The goal effectively ended the match as a contest as Liverpool then dominated possession and left Eddie Howe’s team chasing shadows.
The third goal came in the 68th minute when the hapless Cook turned Andrew Robertson’s cross into his own net before Salah completed his hat-trick with 13 minutes left when he twisted and turned a tiring home defence then slotted the ball home.