The Kop was roaring with delight after seeing their beloved Reds go ahead so early but if they were expecting a rout, they were sorely disappointed for Eddie Howe's men kept their discipline and shape to frustrate the hosts.
Salah's goal comes at the end of a week that has featured plenty of discussion about the race for the Premier League Golden Boot, after Harry Kane was awarded an extra goal for the faintest of faint touches on Christian Eriksen's cross against Stoke last week.
Mohamed Salah doubled the scoring on 69 minutes when Trent Alexander-Arnold produces a wonderful cross and the Egyptian instinctively nodded the ball over the onrushing Begovic.
FRIENDS Salah says whatever happens Roma will be his friend for life
With the win, the Reds close to within a point of second-placed Manchester United, although the Red Devils have two games in hand, but perhaps more importantly, three clear of Tottenham Hotspur.
Liverpool's front three were on the scoresheet, with Salah becoming just the eight player - and the first African - to reach such a landmark in the Premier League era.
The finish puts him on 30 league goals, five more than Kane, who play against Manchester City later on Saturday.
"I think it is always important not to panic during disappointing runs", the Bournemouth boss said.
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