Henderson curled a teasing cross into the penalty area and Mane found a pocket of space inside the Bournemouth area to glance a header at goal which goalkeeper Asmir Begovic parried.
Mane reacted quicker than the visiting players and was able to steer the rebound into the unguarded net –- thus becoming the highest-scoring Senegalese in the Premier League with 44 goals.
Salah had a snap shot wide and curled an effort over the crossbar in the first half, with Rush looking on from among the crowd.
Good to be back home. ?#LIVBOU pic.twitter.com/lQfP7ww52M
— Liverpool FC (@LFC) April 14, 2018
With 21 minutes remaining, Trent Alexander-Arnold curled a high ball from deep and Salah escaped from the attention of Nathan Ake to flick a header over over Begovic and into the net.
It was Salah’s 30th league goal for Liverpool as he found the net for the seventh successive home league match.
Bournemouth briefly threatened when Dan Gosling’s shot brought a smart diving save out of Loris Karius but that was the best they could offer on a day when Liverpool won comfortably without breaking sweat.
Klopp’s side put the gloss on the result in injury time when the tireless Roberto Firmino was rewarded for his persistence and finished calmly at the near post after being found by Alex Oxlade-Chamberlain.