The Egypt winger was slightly below par on this occasion by his lofty standards, but a header 21 minutes from time took him to 40 in all competitions in a Reds shirt and 30 in the league, adding to Sadio Mane’s first-half strike before Roberto Firmino netted a late third.
The Reds – inspired by Salah – booked their place in the Champions League semi-finals with a win at Manchester City on Tuesday, but their attention returned to domestic action in a victory that puts pressure on second-placed rivals Manchester United.
Jurgen Klopp named a full-strength starting XI and it quickly became clear that Bournemouth would not improve on their winless record at Anfield.
It still looked for long periods as though Liverpool would fail to add to the lead secured early by Mane in a one-sided match, but Salah predictably sealed the win to move five clear of Harry Kane in the Golden Boot race ahead of the Tottenham man’s clash with City later in the day.
And Firmino got in on the act in the final stages as Klopp’s side move within a point of United, who have two games in hand.