He has now widened the gap with Tottenham and England striker Harry Kane, who faces leaders Manchester City later in the day, back to five goals at the top of the scoring charts.
The Spain worldwide has impressed under Zinedine Zidane this time out.
The Kop were in a celebratory mood, and those gathered in Anfield also marked tomorrow's anniversary of the Hillsborough Disaster with a respectful minute's applause. We've had to really work hard for all that stuff.
He got it in the 69th, heading a Trent Alexander-Arnold cross over the leaping Begovic.
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. However, the Bosnian couldn't keep hold of it and Mane made the net bulge with a powerful strike of the loose ball.
Bournemouth didn't muster a shot on target in a first half they were second best in throughout, and were delighted to hear Chris Kavanagh's whistle for half-time finding themselves only one goal behind.
The atmosphere was nearly too relaxed inside Anfield. What happened? But we have to stay angry, we play Bournemouth, the rest was a few days ago and I said a few times our whole lives is Champions League qualification, so these games are all so important.More news: Liverpool star James Milner mocks Tottenham Hotspur ace Harry Kane
Virgil van Dijk narrowly cleared the crossbar with a drive from distance; however, chances were proving more hard to come by as Bournemouth regrouped.
Alexander-Arnold whipped in a cross as he had done for his team-mate earlier, and this time Salah was in the mood to score. At nearly no point in the game did anything other than a home win look on the cards, and a routine three points proved inevitable.
During a dominant first half, Liverpool created 10 goalscoring opportunities to Bournemouth's one and Mane's 18th goal of the season ultimately laid the foundations for a comfortable evening.
This livened the place up. Substitute Lys Mousset failed to bundle in an initial cross from close range, while Dan Gosling forced a smart save out of Loris Karius with the follow-up.
Chances then came and went for Liverpool to score a third in the shape of Mane and Roberto Firmino, before Bournemouth nearly found an unlikely route back into the game late on.