And Firmino got in on the act in the final stages as Klopp's side move within a point of United, who have two games in hand.
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.
- Liverpool are unbeaten in their last 19 Premier League home games (W12 D7), the longest current run in the division, and the Reds' longest run since August 2009 (31 games).
Kathua rape and murder: Two BJP cabinet ministers quit
On Saturday, the Bharatiya Janata Party rushed its National General Secretary Ram Madhav to Jammu to firefight the situation. The body of the girl was recovered on January, 17 a week after she went missing while grazing horses in the forest area.
There have been 19 goals scored in the five previous Premier League meetings between these sides, at an average of 3.8 per game.
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.
Bournemouth are lining up in a 4-4-1- system, with veteran striker Jermain Defoe leading the line even as Joshua King starts just behind him.
Salah may not be too concerned - he will reach 40 goals for his club in all competitions this season if he scores against the Cherries.