Antoine Semenyo gave the visitors a stunning third-minute lead but Luis Diaz levelled with a neat finish and before half-time Mohamed Salah tucked in the rebound from his own missed penalty, his 187th Liverpool goal moving him ahead of Steven Gerrard and into fifth in the club’s scoring charts.
Liverpool could have been rocked when Mac Allister was harshly shown a straight red for catching Christie on the foot just before the hour mark, but instead they scored a third moments later as Diogo Jota rifled in a rebound to settle it.
The hosts were fortunate they had not dug themselves an even deeper hole in a chaotic opening few minutes which illustrated the work still ahead as Jurgen Klopp reshapes his side.
With new signing Wataru Endo watching on from the bench after receiving international clearance, the need for such a defensive midfielder was clear as Liverpool repeatedly played themselves into trouble and were made to pay a price by Bournemouth’s energetic press.
The visitors, who have never won a league match at Anfield and who lost here 9-0 12 months ago, thought they had an opener inside 60 seconds as Alisson and Ibrahima Konate both went to try to intercept a long ball down Bournemouth’s left channel, but Jaidon Anthony was offside before tucking the ball in.
No matter, as the opener came two minutes later. Virgil van Dijk played a routine pass to Trent Alexander-Arnold but the England man showed his deficiencies in an inverted role, with a loose touch allowing Philip Billing to prod the ball through for Dominic Solanke.
Andy Robertson prevented the ex-Liverpool man from getting a shot away but the ball fell for Semenyo to thump home.
Van Dijk then headed against the crossbar from Robertson’s corner, briefly lifting the mood inside Anfield before Alisson provided another moment of panic.
The Brazil goalkeeper mis-placed a pass and then felled Anthony just outside the area as he threatened to race through on goal, his punishment limited to a booking with Konate covering.
The brittle nature of Liverpool’s midfield was seen again in the 25th minute when Marcos Senesi strode out of the Bournemouth defence and simply kept going all the way to the final third, slipping in Solanke who was sandwiched by Robertson and Van Dijk but made no great appeal for a penalty.
Moments later, Liverpool were level. Jota’s ball from the right was slightly behind Diaz after Senesi got a touch, but the Colombian adjusted well to control and then fire home from close range.
The penalty came eight minutes later as Dominik Szoboszlai made the most of a dangling leg left by Joe Rothwell and went down in the corner of the box. Neto saved a relatively tame effort from Salah but the Egyptian was there to finish at the second opportunity, his ninth goal in nine against Bournemouth.
Liverpool looked much more settled in a strong start to the second half as Jota and Salah threatened.
It might have all changed when Mac Allister’s home debut was cut short just before the hour, but if anything a sense of injustice fired Liverpool up.
Endo was waiting to come on for his debut in a midfield reshuffle when Neto could only parry a deflected shot from Szoboszlai and Jota tucked in the rebound.
Endo slotted in well as Liverpool adopted a more conservative approach to see the game out, although Alisson still needed to make a fine late saves from Solanke and Hamed Traore to prevent a more nervous finish to the afternoon.