Liverpool’s composed display at Anfield sent Bournemouth to an eighth successive away defeat.
Three days after Manchester City moved top on goal difference, Jurgen Klopp’s side responded in emphatic style to talk that the pressure of a title race was showing in their performances.
After a cagey opening in which Ryan Fraser tested Liverpool goalkeeper Alisson, Sadio Mane settled any nerves by powerfully heading home James Milner’s cross.
Mane, who looked fractionally offside, has now scored in four successive Premier League games for the first time.
Georginio Wijnaldum had not been allowed to stay in the Liverpool hotel on Friday because of illness but he was in fine form, doubling the lead with a sublime lob over the helpless Artur Boruc.
Moments after the break, Naby Keita and Roberto Firmino combined in a move Klopp called “world class” to present Mohamed Salah with a simple finish from 10 yards, his 20th goal in all competitions this season.
Klopp’s side never looked in danger of losing their lead and moved on to 65 points, a tally which would have been enough for at least a nine-point lead at the same stage of the title race in any of the past five seasons.