The Reds are high on confidence after knocking Manchester City out of the Champions League and setting up a semi-final date with Italian giants Roma, but must now get down to the business of nailing down a top four spot in the Premier League.
Mane put in a rebound for his 10th league goal of the season, and Salah continued his player-of-the-year calibre campaign with his 30th.
The Reds got off the flawless start this weekend as they broke the deadlock after seven minutes thanks to a clinical strike from Sadio Mane.
Bournemouth's goalkeeper continued to be kept busy as he pushed away a free-kick from Trent Alexander-Arnold and comfortably held Salah's 25-yard curler.
It was Sadio Mane who opened the scoring for the Reds with just seven minutes gone after receiving a smart pass from Jordan Henderson. His balls in from the right hand side posed a consistent threat to Bournemouth in the first half, before one finally paid off as it reached the head of Mohamed Salah.
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