Any sense Liverpool would be distracted by the looming continental clashes with Roma was banished by Mane's early goal, with Mohamed Salah then netting his 40th of the campaign and Roberto Firmino's late strike ensuring Klopp's side remain on course for a top-four finish.
The Reds, inspired by Salah, booked their place in the UEFA Champions League semi-finals with a win at Manchester City on Wednesday (AEST), but their attention returned to domestic action in a victory that puts pressure on second-placed rival Manchester United.
Although Salah stated he would rather win the Champions League, he still has his eyes on winning both accolades, with Salah admitting that winning the Golden Boot is still on his mind. "I'm sure he'll keep doing that for the rest of the season". He's the first Liverpool player to achieve this since Ian Rush in the 1980s.
Jurgen Klopp's side came into the match on the back of an emphatic 5-1 aggregate victory over Manchester City in the Champions League quarter-finals.
The Egyptian is in pole position to with the Premier League Golden Boot, where he now has a five goal lead over Harry Kane, and he is also chasing Champions League glory with Liverpool after the club progressed to the semi-finals.
"He could have had a few today but he kept going and kept going and got his goal in the end". It's also very close, it's just seven goals. Now we still have four games and they (Tottenham) have five games so I have to think about my games and we see. "I can not lie - it is in my mind", he explained. "I will try my best to score again and help the team".
"I am happy to have this feeling". That is the most important thing for us, that we play as a team, we play as 11 players.
Bournemouth had contained Salah well until he finally scored 21 minutes from time, drifting behind Nathan Ake and heading in Trent Alexander-Arnold's cross in the 3-0 win.