Match ends, Bournemouth 0, Liverpool 4.
Mohamed Salah scored a hat-trick against Bournemouth to send Liverpool to the top of the table - then handed his man-of-the-match award to team-mate James Milner.
Former England midfielder Milner became the 13th player to make 500 Premier League appearances when he captained Liverpool against the Cherries.
When handed his award after the game, Salah opted to give it to Milner and told Sky Sports: "I will not take it.
"Congratulations on his amazing career. He deserved it today. I hope we'll win something together."
Salah scored his second hat-trick for the club since arriving from Roma 18 months ago as Jurgen Klopp's side went one point clear of Manchester City, who later suffered their first top-flight defeat of the season as they lost 2-0 at Chelsea.
Salah was in an offside position when Roberto Firmino hit a 30-yard shot that home keeper Asmir Begovic carelessly pushed out in the direction of the Egypt forward. He finished clinically and his eighth top-flight goal of the season was allowed to stand to break the deadlock in a game the visitors dominated from the start.
There was nothing fortuitous about the Liverpool forward's second though, a composed finish after driving at the Bournemouth defence, before Steve Cook backheeled the ball into his own net while attempting a clearance to make it 3-0.
Salah then completed his hat-trick after rounding Begovic, cutting back to beat the Bournemouth keeper for a second time and poking the ball past Nathan Ake on the line.
"Whatever you do in a football game, you need somebody to finish it off and what Mo did with his two goals in the second half was exceptional," said Klopp after his side's fifth straight league win.
Liverpool have taken 45 points from the past 51 on offer and are unbeaten in 17 league games in a run that stretches back to last season.
- Quiz: Can you name the players who have made 500 Premier League appearances?
- What happened in the Premier League on Saturday?
- Reaction from the Vitality Stadium
Salah back to best at start of huge week
The wins keep coming for Liverpool - and the goals are flowing once again for Salah.
Having successfully negotiated a bruising night at Burnley on Wednesday, Klopp's side started a huge week by ruthlessly dismantling Bournemouth.
Salah goes into Tuesday's Champions League must-win group game with Napoli having marked his return to the starting line-up by emphatically ending a three-match run without a goal.
Bournemouth have every right to feel disgruntled about the former Chelsea player's first, with television replays clearly showing Salah was offside when Firmino struck the shot that Begovic spilled into his path.
Yet the hosts can have few complaints about his second or third.
Despite Cook's attempt to bring him down, Salah stayed on his feet to drive at Bournemouth's defence before producing a neat finish into the corner via a slight deflection off Ake.
Cook's troubled game continued when the Bournemouth defender inadvertently diverted the ball into his own net following a cross by Andy Robertson, before Salah completed the rout.
After shrugging Cook off the ball following substitute Adam Lallana's long punt forward, Salah dribbled into the box before tormenting Begovic and slotting home.
After the game, Bournemouth boss Eddie Howe described Salah as "one of the best in the world".
"Salah looked very good, razor sharp and we struggled to handle him. He played more centrally and did well from that position," he said.
While the headlines belong to Salah, Liverpool overcame the absences of injured defensive trio Joe Gomez, Dejan Lovren and Nathaniel Clyne to record a 10th Premier League clean sheet of the season before next Sunday's visit of Manchester United to Anfield.
Bournemouth come unstuck against top six - again
Bournemouth started the weekend seventh in the table - level on points with sixth-placed Everton - and with plaudits ringing in Howe's ears.
Their climb from League Two to the fringes of European qualification in 10 seasons is nothing short of phenomenal, but the Cherries were second best all over the pitch against Liverpool.
This scenario is becoming a familiar story for the Dorset club against the league's leading sides.
Howe's team are regularly praised for producing attractive, progressive football - but their record against the top-six teams is extremely poor.
Since the start of 2017-18, Bournemouth have lost 15 times in 17 games against Manchester City, Liverpool, Arsenal, Chelsea, Tottenham and Manchester United.
The bad news is they still have to face Tottenham and United - both away - in the league this month.
They were not helped by the absence of leading scorer Callum Wilson because of a hamstring injury, but the England striker would not have helped their defence - now without a clean sheet in seven league and cup games - contain Liverpool.
500 not out for Milner
This was a momentous day for Milner.
With Jordan Henderson on the bench, Milner captained Liverpool to victory in a game in which his statistics were again impressive.
Having covered 12.57 kilometres at Burnley in midweek - more than any other player on the pitch - the 32-year-old clocked up another 11.73 filling in at right-back against Bournemouth.
There was one nervous moment when his misplaced first-half pass required Alisson to dash out of his goal to head clear - and in doing so, taking out Joshua King.
But Milner was otherwise a reassuring presence in the back four, demonstrating his value to Klopp with his ability to move from midfield to full-back and give youngster Trent Alexander-Arnold a rest with Gomez injured.
In fact the Yorkshireman found himself in the Bournemouth half as often as he was his own as he played a significant part in the 238th top-flight win of his career.
Man of the match - Mohamed Salah (Liverpool)
'Another game that has gone away from us' - the managers
Bournemouth boss Eddie Howe: "I have many complaints. He [Salah] was offside [for the first goal]. It has a huge bearing on the match. We were fine until that moment. It changes the game.
"It was difficult for us losing Callum Wilson. We have to deal with players who aren't here and can't use that as an excuse. We still had a competitive team on the pitch.
"The first goal is key and then we made some mistakes at bad times.
"At half-time I thought we were well in this match. I expected a very different second half. We just had to manage the scoreline. It is a tough league. We are disappointed as it's another game that has gone away from us."
Liverpool manager Jurgen Klopp: "It is clear that everyone knows about the quality of Bournemouth.
"We had to keep the ball and win the ball back as quickly as possible. We did both very often but not always as they had their moments too, of course.
"I don't know if it was offside. I've not watched it back but we improved in the second half and controlled the game. It was really nice. Mo Salah scores that goal [the second one] and I don't think many do in that situation.
"The third goal was again brilliant. It is really cool and it helps of course! We played nice football and the players we brought on did really well."
Own goal misery for Cherries - the stats
- Since the start of 2015-16, Bournemouth have scored more own goals in the Premier League (eight) than any other side currently in the top flight.
- Liverpool have accrued 42 points from their opening 16 league games of the season, their best tally at this stage of a top-flight campaign.
- Howe has lost more games in all competitions against Liverpool than against any other side (eight).
- Begovic has made eight errors leading directly to a goal in the Premier League since the start of 2017-18, more than any other player.
- Bournemouth's Jefferson Lerma has been shown 22 yellow cards in the Premier League since the start of last season, more than any other player in Europe's big five leagues (38 apps).
- Salah's opener was his 40th goal in his 52nd Premier League appearance for Liverpool, the fastest a player has reached that milestone in the competition for the Reds (Fernando Torres 60, Daniel Sturridge 64).
- Since the start of last season, only Lionel Messi (43) has scored more league goals in the big five European leagues than Salah (42).
- Salah is only the second Liverpool player to score a competitive hat-trick against Bournemouth after Harry Chambers in the FA Cup in January 1927.
- Alisson has remained unbeaten in his opening 16 league matches as a Liverpool player, which is a club record as it moves him ahead of Javier Mascherano (15, set in November 2007).
Bournemouth take on Wolverhampton Wanderers (15:00 GMT) next Saturday while Liverpool have back-to-back home games against Napoli in the Champions League on Tuesday (20:00) and Manchester United in the Premier League next Sunday (16:00).
- 3S Cook
- 5AkéBooked at 12mins
- 11DanielsSubstituted forRicoat 83'minutes
- 20BrooksSubstituted forMoussetat 65'minutes
- 8LermaBooked at 15mins
- 19StanislasSubstituted forMingsat 83'minutes
- 4van Dijk
- 23ShaqiriSubstituted forManéat 65'minutes
- 3FabinhoBooked at 70mins
- 8KeitaSubstituted forLallanaat 65'minutes
- 9FirminoSubstituted forHendersonat 81'minutes
- Lee Mason
- Shots on Target
Second Half ends, Bournemouth 0, Liverpool 4.
Sadio Mané (Liverpool) wins a free kick in the attacking half.
Foul by Andrew Surman (Bournemouth).
Foul by James Milner (Liverpool).
Diego Rico (Bournemouth) wins a free kick in the defensive half.
James Milner (Liverpool) wins a free kick in the defensive half.
Foul by Diego Rico (Bournemouth).
Foul by Jordan Henderson (Liverpool).
Jefferson Lerma (Bournemouth) wins a free kick in the defensive half.
Delay over. They are ready to continue.
Delay in match Adam Lallana (Liverpool) because of an injury.
Adam Lallana (Liverpool) wins a free kick on the left wing.
Foul by Jefferson Lerma (Bournemouth).
Attempt missed. Georginio Wijnaldum (Liverpool) header from the centre of the box misses to the right. Assisted by Andrew Robertson with a cross following a corner.
Corner, Liverpool. Conceded by Simon Francis.
Attempt missed. James Milner (Liverpool) right footed shot from outside the box misses to the left. Assisted by Georginio Wijnaldum.
Substitution, Bournemouth. Diego Rico replaces Charlie Daniels.
Substitution, Bournemouth. Tyrone Mings replaces Junior Stanislas.
Substitution, Liverpool. Jordan Henderson replaces Roberto Firmino.