Summer signing Alexis Mac Allister was sent off in his first home match for Liverpool but the Reds still overpowered Bournemouth in a thrilling Premier League match at Anfield.
The Cherries, who had already had a goal disallowed because Jaidon Anthony was offside, scored inside three minutes when the Reds gave away possession and Antoine Semenyo fired into the bottom corner.
Jurgen Klopp's side eventually got into their stride in a frantic first half and scored twice in an eight-minute period.
Luis Diaz got the equaliser when he collected Diogo Jota's low cross, flicked the ball up, spun and volleyed home.