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.
Liverpool forward Mohamed Salah has insisted that he would happily trade in the personal honours heading his way in exchange for Champions League success.
Asked whether he would prefer to win the Champions League or an individual honour like the golden boot, Salah replied: "If you had a choice between the Champions League and (individual honours like the golden boot) then of course the Champions League".
Liverpool face Roma in the semi-finals of the Champions League and ex-Reds stopper Bruce Grobbelaar is tipping them to go the whole way. "I'm sure he'll keep doing that for the rest of the season".
"What a number. Wow!" exclaimed manager Jurgen Klopp on hearing Salah is the first Liverpool player since Ian Rush 31 years ago to score 40 in a season.
"Of course the Champions League".
Salah has enjoyed an incredible debut season at Liverpool in the league and the European competition.
"So each goal for me, or for anyone else is to try to help the team".
Their dominance in possession should have led to more goals for the break, Trent Alexander-Arnold close with a free-kick whilst Nathan Ake did well to sniff out chances for Premier League top scorer Salah.
But, with potentially seven games remaining for his team, Salah may yet challenge Rush's all-time club record - 47 goals in a blistering 1983-84 campaign. "I can not lie - it is in my mind", he explained.
Liverpool midfielder Alex Oxlade-Chamberlain has described Mohamed Salah's goal against Bournemouth as "unusual". But even in the end I said it - I try to score every game to help the team.
"He tried to motivate us like usually and in the end everybody was in the right place at the right time to win every ball".