The Egyptian worldwide is now leading the race for the Golden Boot, while his teammates Roberto Firmino (12), Philippe Coutinho (9) and Sadio Mane (7) have also been chipping in across all competitions.
Jurgen Klopp has made four changes to his XI, with the England global coming in for the Senegalese speedster and Jordan Henderson replacing a suspended Emre Can in midfield.
The Reds opened the scoring through midfield maestro Philippe Coutinho following a mazy run. Coutinho dribbled at speed down the left, cut inside Simon Francis and slotted a fine effort inside the near post after beating Lewis Cook.
Firmino nearly doubled that lead with an effort which deflected wide after excellent work by the ever-dangerous Salah.
Coutinho was also asked about whether his first-half goal was his best ever strike for Liverpool, but focused more on the benefit of getting back to winning ways after successive draws.
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On Sept. 3, Little Rocket Man replied by detonating a hydrogen bomb northeast of Pyongyang - North Korea's most powerful nuclear test ever .
Junior Stanislas' arrival to replace the injured Josh King finally sparked some life in Bournemouth, and the 28-year-old quickly sent Jermain Defoe haring through on goal.
Begovic then denied Liverpool what would have been a stunning goal when Coutinho flicked a ball over the defence for Salah, who shot straight at the goalkeeper.
It was 3-0 to Liverpool before half-time and Salah had twice before cut in on his left foot and looked for the far corner.
Firmino added a facile fourth when nudging home Coutinho's whipped cross before the game meandered to its close.
Replacement Ryan Fraser blasted wide and Daniels trudged off injured for Bournemouth after the break, before Alex Oxlade-Chamberlain struck a post for the visitors.