The victory rounded off a fine week for Liverpool, who booked a Champions League semi-final against Roma by beating Manchester City 5-1 on aggregate with a second-leg win at the Etihad Stadium on Tuesday.
He also remains in the running to become the PFA Player of the Year as his battle with Manchester City's Kevin de Bruyne is set to go down to the wire.
Roberto Firmino then rounded off a ideal afternoon for Liverpool's prolific front three by drilling low past Begovic for a third in stoppage time.
Jurgen Klopp, Manager of Liverpool celebrates victory with Alex Oxlade-Chamberlain of Liverpool after the Premier League match between Liverpool and AFC Bournemouth at Anfield on April 14, 2018 in Liverpool, England.
"It is incredible that Salah has achieved so much and could be the difference between Liverpool winning the Champions League or not - that is how important he is to them", Murphy told BBC Sport.
Salah is just the third player in Liverpool's history to score 40 goals in a season, joining Roger Hunt and Ian Rush, and the latter's club record of 47 is the next feat in his sights.
Asked whether he would prefer to win the Champions League or an individual honour, Salah said: "If you had a choice, then of course the Champions League".
Now, unless you've been living under a rock, you will know that Tottenham striker Harry Kane was bafflingly awarded Christian Eriksen's goal against Stoke last weekend, despite replays indicating he got no touch on it whatsoever.
Less encouraging is the situation regarding Emre Can, whose participation for the rest of the season may depend on the club reaching the Champions League final in Kiev at the end of May.
There was a sense this might not be Salah's day when he failed, correctly, to win a penalty moments before his goal. "And what a number we scored as a team in the whole season, that's insane".
"It's also very close, it's just seven goals but let's see", he added.
In the second half Mohamed Salah met Trent Alexander-Arnold's lofted cross brilliantly, looping a header over the Cherries keeper, for a second before Roberto Firmino secured the points with a third on 90 minutes.