Image caption, Kai Havertz scored after an error from Alisson, the Liverpool goalkeeper ByAadam Patel, Football reporter at Anfield and Alex Howell, Football reporter Published 1 minute ago Kai Havertz's first-half goal made the difference as Arsenal won at Anfield in the Premier League for the first time since 2012.

Here's how we rated the Liverpool and Arsenal players, and your scores are below.

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Published 21 August Liverpool Alisson: It was his error - a poor pass out - that led to Havertz giving Arsenal the lead.

Made a great save to deny Christos Tzolis but that mistake ultimately proved costly.

4 Ronald Araujo: Made his 12th consecutive start.

Battled well as ever but was given a really tough test by Tzolis down Arsenal's left.

6 Jeremy Jacquet: Shaky in patches but had a decent game on the whole and made a superb tackle after slipping in the second half.

6 Virgil van Dijk: Reliable as ever but will be so disappointed with how easily Liverpool gifted Arsenal the lead.

6 Milos Kerkez: Had a frustrating first half but delivered a lovely cross which Alexis Mac Allister should have headed in.

5 Trey Nyoni: A real show of faith from Andoni Iraola to give the 19-year-old his first Premier League start.

Looked a bit nervy early on but grew into the game.

6 Alexis Mac Allister: Constantly involved in the first half but will know that he should have scored when Kerkez found him.

6 Bradley Barcola: Started down his preferred left flank and caused Arsenal plenty of problems, though he is still waiting for a first Premier League goal.

7 Florian Wirtz: Hit the bar with a great free-kick in the first half, but a player with his price tag simply has to do more in big games.

6 Cody Gakpo: Looked lively initially, but Riccardo Calafiori dealt with him very well.

Could have had a penalty, but the appeal was waved away by Andy Madley.

5 Alexander Isak: Got in some good positions but couldn't find the net.

Unlucky not to get a penalty when his shirt was pulled by Timber.

5 Subs: Szoboszlai (on 59, Nyoni): Back after a spell on the sidelines.

6 Ngumoha (on 67, Gakpo): Didn't get on the ball as much as he would have liked.

5 Munoz (on 82, Araujo): Tried to make an impact with his pace.

Koumas (on 82, Wirtz): Thrown on to add some energy.

Tsimikas (on 82, Kerkez): Didn't have much luck down the left.

Subs not used: Mamardashvili, Gomez, Endo, Gravenberch.

Arsenal David Raya: Made a good clearance after a ball was played through the Arsenal defence in the first half.

The usual assured performance from the goalkeeper.

7 Jurrien Timber: Involved in a very good battle with Barcola and had to deal with a lot of attacks down the right side.

Perhaps lucky to not give away a penalty for a shirt pull on Isak.

7 Ezri Konsa: Continued his recent good form and was solid in the middle of the Arsenal back four.

8 Gabriel Magalhaes: Dealt with the threat of Isak and led the Arsenal backline.

8 Riccardo Calafiori: Not allowed to attack as much as usual but a solid defensive performance from the left-back.

8 Declan Rice: The midfielder provided the assist for Havertz's goal and was Arsenal's best player.

His energy in midfield was a big reason the Gunners won the game.

8 Bruno Guimaraes: An all-action display and involved in the move for the Arsenal goal.

Subbed just after an hour.

6 Martin Odegaard: Won the ball back which started the move for the Arsenal opener.

6 Noni Madueke: Heavily involved in the opening goal as he started after shaking off a knock.

Tired as the game went on.

6 Christos Tzolis: The winger's first start since September after injury and provided a threat from the left.

Forced Alisson into an excellent save with a curling effort.

6 Kai Havertz: Scored the only goal of the game, which he needed after a difficult couple of matches.

Put himself about and linked the play.

7 Subs: Myles Lewis-Skelly (on 62, Guimaraes): Came on and helped to calm the game down for Arsenal as Liverpool pushed for an equaliser.

7 Piero Hincapie (on 84, Tzolis): Brought on to see out the win.

6 Viktor Gyokeres (on 84, Havertz): Introduced to provide a threat behind the backline.

6 Merino (on 88, Odegaard): Added defensive strength for the closing minutes.

Subs not used: Arrizabalaga, Mosquera, White, Eze, Zubimendi.

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1 Give it up 10 Pure perfection Liverpool (active) Arsenal Starting XI Number: 1 Alisson Becker Number: 6 M.

Kerkez Number: 4 V. van Dijk Number: 5 J.

Jacquet Number: 33 R.

Araujo Number: 42 T.

Nyoni Number: 10 A.

Mac Allister Number: 29 B.

Barcola Number: 7 F.

Wirtz Number: 18 C.

Gakpo Number: 9 A.

Isak Substitutes Number: 67 L.

Koumas Number: 23 Víctor Muñoz Number: 73 R.

Ngumoha Number: 8 D.

Szoboszlai Number: 21 K.

Tsimikas Back to team tabs Starting XI Number: 1 David Raya Number: 33 R.

Calafiori Number: 6 Gabriel Magalhães Number: 15 E.

Konsa Number: 12 J.

Timber Number: 39 Bruno Guimarães Number: 41 D.

Rice Number: 17 C.

Tzolis Number: 8 M. Ødegaard Number: 20 N.

Madueke Number: 29 K.

Havertz Substitutes Number: 14 V.

Gyökeres Number: 5 P.

Hincapié Number: 49 M.

Lewis-Skelly Number: 23 Mikel Merino Back to team tabs After the opportunity to rate players has closed, the score displayed represents the average from all the submissions by BBC Sport users.