Diaz was electric in the first half, papering over Liverpool's defensive frailties with a brilliant attacking display from the left wing that overpowered the visitors, with the game effectively over as a contest by halftime.
Arne Slot's side had the VAR to thank for chalking off an early Bournemouth goal from Antoine Semneyo due to offside, with the groans of the home fans who feared another shock defeat turning to whoops of joy as the goal was overturned.
The electric Diaz then went to work, forcing keeper Kepa Arrizabalaga into a fine save in the eighth minute, and he threatened several more times before finally beating Kepa to a long ball and rattling it home in the 26th minute.
Less than three minutes later Diaz had his second goal as Bournemouth were sliced open by a five-on-four break, the Colombian using his left foot to drive the ball between the legs of the advancing Kepa for his fifth goal in five league games.
Darwin Nunez then added a brilliant third, attacking down the right and slowing down before suddenly accelerating again to cut inside and curl home a left-foot shot to make it 3-0.
With the game out of the visitors' reach, there was little of note in the second half save for the Premier League debut of Liverpool's Enrico Chiesa, who came off the bench and provided a glimpse of the talent that prompted the Merseysiders to pay Juventus a reputed £10m for him.
Despite their offensive dominance, Liverpool still looked occasionally vulnerable at the back and keeper Caoimhin Kelleher had to claw away the ball after it hit the bar from a late corner, but Bournemouth could not find a way back into the game and the hosts ran out easy winners.
