- Listen to Bournemouth v Liverpool on 5 live & online
- Salah puts away rebound for lead - replays show he was offside; Egyptian sweeps in second
- Cook inadvertently backheels into his own net, Salah dances past Cherries defence for his hat-trick
- Liverpool go top of league - Man City can regain top spot when they face Chelsea at 17:30 GMT
- Bournemouth now lost five of last six
- Get involved using #bbcfootball
So this is how things stand at the top of the Premier League table. Liverpool are a point clear of Man City who play Chelsea at 17:30 GMT.Copyright: BBC
Liverpool manager Jurgen Klopp speaking to Match of the Day: "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.
"The whole game was brilliant from him [Salah] today - not only the goals. He wanted to help with runs in behind and him scoring three goals is big for him and very important for us."
On substitutes keeping up intensity: "It is nice. I really like that. Adam Lallana has not played for so long. Jordan Henderson was playing one-twos. It was really good. We want to enjoy it for as long as we can."
On huge week: "It is always a huge week. Napoli is a tough one and then Man United - we all know what can happen there. Hopefully we can stay fit. Let's go for it!"
Bournemouth manager Eddie Howe speaking to Match of the Day: "I have many complaints. He [Mo 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 score-line. It is a tough league. We are disappointed as it's another game that has gone away from us.
On Liverpool's title hopes: "Liverpool are very good. It is a very competitive league this year. I think it will go until the end. Manchester City, Liverpool and I think other teams will challenge too. It should be an entertaining end."
Former England defender on Final Score
Considering they haven't been at full steam Liverpool, to still be in touching distance of a team like Man City, it's just about hanging in there now.
Liverpool host Man United and Arsenal before beginning 2019 against Man City...
Liverpool manager Jurgen Klopp, speaking to Sky Sports: "It was a very mature game. It was a very controlled first half, we scored a goal and controlled the game. We were not completely happy with the rhythm. We made changes and wanted to do more but there was a lot of good counter pressing.
"Mo scored a fantastic second goal. He did brilliantly and the fourth one was brilliant, completely calm. Then Adam (Lallana) and (Sadio) Mane come on and we played brilliant football that was exactly as we wanted.
"Bournemouth have had a really good season, coming here, winning in the manner we did was quite special.
On Mo Salah's performance: "It was absolutely brilliant. From the first moment if he could play in behind was there. He was on fire. It is nice for him to score three goals. We know how big his desire is.
On the title race: "We want to be as good possible at the end of the season. It is not clear what that is. I think the only way to be successful is to be completely focussed on yourself.
"We are not really interested on other teams. We only have three days until Napoli which is a big one. It is Bournemouth celebrating day. Let's go home, have food and go again."
James Milner speaking to Match of the Day: "I think it is about finding a way to win. Mo Salah was outstanding and we did the job well in a pretty place to come. We need to keep going.
"He [Salah] is a top player. In times when it is tight and things aren't quite going the way you want, you need the big players to take the game by the scruff. He did that today. He is a massive player for us. We have that quality right throughout the squad.
On playing at right-back: "It was different again but you do what's required. It gives Trent [Alexander-Arnold] a little rest. It was nice to be a part of that performance and get another win on the road.
On being top of the table: "It is nice to see. It is where you want to be at the end of the season. There is a long way to go. We know how crucial Christmas is."
Peter: Watching Salah's third goal again reminds of when Liverpool had Balotelli and Benteke, who regularly rounded the keeper and missed open goals. Huge difference in quality these days
Kyle: As well as playing some superb football the work rate and the defending from Liverpool has again been outstanding. When you have that you always have a great chance. Their a joy to watch
Mohamed Salah speaking to Sky Sports: "Scored three goals, went top of the table and kept a clean sheet. It was a fantastic result. I enjoyed the last one the most. I was calm.
"i know everyone has high expectations for me but the most important thing is to win each game and that we are top of the table.
"I have to congratulate him for his amazing career. I hope I have more games like this in my career. But I will not take it [the award from Milner]."
Mo Salah is given the man of the match by Sky Sports but refuses to accept it and instead hands the award to James Milner to mark the Englishman's 500th Premier League appearance.
We'll have reaction from the players and managers shortly.
Stick around for that or follow build-up to the 15:00 kick-offs here.
Brighton coach on BBC Radio 5 live
It's fully deserved today's result. You can tell they've enjoyed it and it puts the pressure right back on Manchester City.
It was such a sloppy start to the second half by Bournemouth. Eddie Howe will be fuming, they were left facing a huge uphill battle.
Mo Salah was devastating and defensively they were so strong too. Look at the subs Jurgen Klopp has made too - they have a very strong squad now. If they can keep this up, we've got a really good title challenge on our hands.
Salah grabs hold of that match ball and holds it tightly to his chest before applauding the away fans.
I wouldn't say the Egyptian looked over the moon but it's a job very well done today.Copyright: Reuters
Over to you, Manchester City.
Mohamed Salah puts Liverpool top of the Premier League with a hat-trick.
BBC Sport at Vitality Stadium
Adam Lallana was on Bournemouth's books as a schoolboy before being prised away by Southampton at age 14 in a deal which eventually brought the Cherries a hefty sell-on fee when he moved from St Mary's to Anfield.
I'd imagine he'll have a few family members here today - who've seen him come on as a late sub and get his head bashed in. Not a happy homecoming, but Liverpool's result should make up for it.
To their credit, most of the Bournemouth fans have stuck around to the end. The Cherries have just been beaten by the better team.
A minute left.
Brighton coach on BBC Radio 5 live
Jurgen Klopp is giving a huge applause to Robertson and Lallana for still tracking back so late into this game.
You'll Never Walk Alone echos around the Vitality Stadium. Liverpool are heading back to the top of the pile.
Lallana is finally back in a shirt with no number or name.