Hamstrung at home, Liverpool continued to run riot on the road as Philippe Coutinho inspired a devastating display of counter-attacking football.
Jurgen Klopp’s side have been held to frustrating draws in their last two matches at Anfield.
But with Bournemouth forced to try and play football on their own patch, the brilliant Brazilian and his team-mates were simply unplayable as they ran and pressed their way back into the top four.
Liverpool will be hoping Barcelona weren’t watching.
Since the Tottenham debacle on October 22, Liverpool have netted 19 goals in five away games, including nine in their last two visits to the South Coast. The last time Liverpool scored three goals or more in five consecutive away games was in 1982.
And that is now 12 unbeaten since Wembley. But the stats do not tell the whole story of a free-flowing performance – admittedly against a free-falling Bournemouth side.
There was no Fab Four with Sadio Mane rested. Instead there was a Fearsome Five of attacking talent, including Alex Oxlade-Chamberlain, who was outstanding in a central role. Even Dejan Lovren, who scored a spectacular diving header, looked like a world-beater.
But Coutinho was the Special One with the stunning opening goal, two assists, and a free-kick against the post.
Barcelona failed with three bids for his services over the summer and his brief post-match interview with Sky suggested he won’t be here forever.
Reds fans really should enjoy him while they still can.
Eddie Howe’s side were served notice that Coutinho (right) was in the mood when his 11th-minute free-kick thudded against the post. But the Brazilian did not have to wait too long to find the net. After 20 minutes, he picked up a Ragnar Klavan pass and exchanged passes with Andy Robertson.
As the Scot continued his run down the Liverpool left, Coutinho used him as a decoy and cut inside before sliding home his 11th of the season.
Coutinho’s corner set up the second six minutes later. Georginio Wijnaldum helped on the ball at the near post and Roberto Firmino hooked the ball back into the six-yard box for Lovren to dive forward to head home.
The Cherries should have pulled one back when Junior Stanislas sent Jermain Defoe clean through but the England striker’s shot hit the inside of the post.
Mo Salah was denied a goal-of-the-season contender at the other end after Asmir Begovic blocked his volley after a perfect sand wedge of a pass from Coutinho. But the Egyptian scored his 20th goal of his remarkable season a minute later when he received Oxlade-Chamberlain’s pass and flummoxed Charlie Daniels before curling a shot home.
Liverpool gave up a three-goal lead in Seville – and contrived to lose from 3-1 up with 15 minutes to go here last year. There was to be no repeat.
Liverpool have lost only one game in 23 to teams outside the top six despite Klopp (right) making another four changes. Bournemouth, who have now gone six games without a win, played an open style pleasing on the eye but less healthy for the goal difference.
After Oxlade-Chamberlain hit the post after the break, Firmino was borderline onside as he nodded home Coutinho’s 66th-minute cross before injury-hit duo Adam Lallana and Danny Ings added to the feelgood factor by coming on for late appearances.