Liverpool looked the likelier scorers as the match went on, and it was no surprise when Salah struck again with two minutes of the second half played.
Salah was the first to threaten as Liverpool settled quickly into the blustery conditions on the South coast, latching on to Xherdan Shaqiri's chipped ball forward but then slicing his right-footed effort wildly off target.
"It wasn't our best performance of the season by any means but we were efficient, got the job done and this fella (Salah) is unbelievable".
Pretty much [it was a flawless result].
'It's a big blow, especially with the form he's been in this season, his athleticism, pace and strength is always a real weapon for us.
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"But as I said before, the most important thing is we are top of the table". But I know everyone else's expectation for me is very high.
After an even opening, Bournemouth went mightily close to the first goal, as David Brooks was released into the left side of the penalty area and Alisson stopped the shot squeezing inside his near post. It was not the most impressive finish but I would say it was pretty surprising [for the goalkeeper].
"Together with Virgil he's improved so much".
"I think I said a few years ago that we have to write our own history", Klopp said. Only one player in Europe has more league strikes since the start of last season: Lionel Messi.
Three minutes after the break, Salah doubled the lead when Bournemouth's Steve Cook was dispossessed in midfield and the Egyptian finished neatly into the far corner. "We were very controlled in the first half, scored the goal but I wasn't completely happy with the rhythm changes".
But while the result allowed him to relish his achievement, the No. 7 was quick to stress that the Reds need to keep momentum going with clashes at home to Napoli and Man United to follow in the next week.