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Much has changed at Liverpool this season, and most of it for the worse, but their supremacy on Merseyside remains.Jurgen Klopp’s side have had their struggles since the turn of the year, but they were too good for Everton here at Anfield, and the hope will be that this 2-0 derby win can inject some momentum into a stuttering campaign.Victory came courtesy of a first-half strike from Mohamed Salah and a first Reds goal for Cody Gakpo after the break - both of them the result of lightning-quick counter-attacks. Everton, who arrived buoyed by their win over Arsenal last time out, offered precious little in response and their new manager, Sean Dyche, knows they still face a serious battle to avoid relegation this season. Defeat leaves the Toffees third from bottom in the Premier League, while Liverpool climb above fellow underperformers Chelsea into ninth.<script type="application/json" data-placement="fcplayer-semantic">{"type":"fcplayer-semantic","data":{"embedCode":"//cdn.fcp.codes/embed-code-template/embed-code-template.js#SEMANTIC_5704afb8-c10b-4ba5-9cb4-d7fb6098ef90"}}</script>Here are the winners and losers from an eventful night…

Welcome to Liverpool, Cody Gakpo! Winners, losers and ratings as brilliant Stefan Bajcetic runs Everton ragged in Merseyside derby

Premier League

Everton

Brentford

Southampton

Mohamed Salah:Thirteen seconds. That was all it took to turn panic into delirium, and end a goal drought that was starting to get more than a little worrying for Liverpool’s Egyptian King. Everton thought they had the lead when James Tarkowski climbed highest to meet Alex Iwobi’s high, hanging corner in the 35th minute, but by the time the clock struck 36 they were behind. Tarkowski’s header hit the post, Liverpool broke and Darwin Nunez picked the perfect pass for Salah, <a href="https://www.goal.com/en/news/watch-what-was-pickford-doing-mohamed-salah-freakish-merseyside-derby-opener-embarrass-everton-stopper/blt0b097a1c32bfea38" target="_blank">who took advantage of some woeful positioning from Jordan Pickford to prod in his 18th goal of the season</a>, and spark wild celebrations on the Kop. He had a hand in his side’s second goal too, his pass allowing Trent Alexander-Arnold <a href="https://www.goal.com/en/news/watch-cody-gakpo-taps-home-first-ever-liverpool-goal-liverpool-cruise-merseyside-derby/blta41218ed89863d76" target="_blank">to set up Gakpo for a far-post tap-in</a>, and while he was unable to inflict further damage, Klopp will have been delighted to see his star man back on the scoresheet, and back smiling.Cody Gakpo:And on the seventh day, Liverpool’s new boy introduced himself properly. It’s been a tough start to life at Anfield for Gakpo, but he’ll have gone to bed with a great big smile on his face tonight, having grabbed his first Reds goal, and in the game which matters most to his new supporters. The Dutchman was perfectly-placed at the far post to tap home Alexander-Arnold’s immaculate low cross and give his side what proved to be an unassailable two-goal lead. The relief was clear on the 23-year-old’s face, and also in his performance across the next half hour, as he tore into Everton with the kind of confidence, purpose and quality we associated with him in his time at PSV Eindhoven. He left to a standing ovation, and a bear hug from Klopp. Job done. The first one is usually the hardest, now we can really start to see what the £44 million ($53m) man is made of.Stefan Bajcetic:Liverpool’s present and its future, all wrapped up in one very special young footballer. To boss a game like this at 18 takes some doing, but Bajcetic accomplished it. He was brilliant from start to finish, reading the game expertly, taking the ball anywhere and tackling like it meant something. One challenge, on Alex Iwobi, led to Liverpool’s second goal, another interception and forward burst should have led to another for Salah. Everton, in Abdoulaye Doucoure, Idrissa Gueye and the highly-rated Amadou Onana, had legs and experience in midfield, but Liverpool had the game’s best player, with Bajcetic’s calmness and class bringing out improvement in both Jordan Henderson and Fabinho, who had their best games for a while. Older fans may remember a teenager called Billy Kenny dominating a derby match for Everton back in the early days of the Premier League. He was never able to fulfil his rich potential, as it turned out, but hopes are high that Bajcetic can become a star for Liverpool. Here, we saw why everyone at Anfield is so excited by him.

The Winners

Jordan Pickford:Where was he going? What was he thinking? The Everton goalkeeper doesn’t have great memories of Anfield, and he won’t want to remember his latest visit in a hurry either. It was his error that opened the game up. The England international is always keen to get himself involved, but he badly misjudged his charge from the line as Liverpool broke, nine minutes before half-time. With Pickford in no man’s land, Salah had the simple task of poking the opening goal home. Everton never recovered, and though Pickford made a couple of decent saves to deny Nunez and Salah in the second half, he made a fool of himself again late on, rushing out of his goal to confront Andy Robertson, who simply laughed in response. A yellow card, to go with another derby howler. Pickford won’t want to return any time soon.Ellis Simms:As one youngster thrived in the cut and thrust of a derby, so another faded into the background. Simms was a surprise choice by Dyche to lead the line for Everton. The 22-year-old had only started one Premier League game before this one, and had spent the first four months of this season on loan at Sunderland in the Championship. But with Dominic Calvert-Lewin injured - again - Dyche overlooked both Neal Maupay and Demarai Gray and went with the wildcard option. It didn’t pay off. Simms looked out of his depth against Joe Gomez and Joel Matip, with Everton offering zero by way of attacking threat as a result. He lasted an hour before being replaced by Gray - an indictment of Maupay’s struggles, to say the least - and it will be a surprise if we see him in a game of this size again any time soon. Everton need Calvert-Lewin back sharpish.Sean Dyche:Maybe Dycheball isn’t all that hard to stop after all. After the joy of Arsenal, Evertonians were brought back down to earth here, reminded that while they may have a new manager who bans hats and snoods and makes them train with long socks and shinpads, they also have a team that lacks balance and quality, and which has been in and around the relegation zone for more than 12 months. Dyche may reflect on fine margins - how different the world may look had Tarkowski’s header dropped in - but he will know deep down that Everton were second best in all departments here. What will hurt him most is that they were outbattled as well as outplayed.&nbsp;He has a job on his hands to keep this side up. Leeds on Saturday is huge.

The Losers

Alisson Becker (6/10): Did what he had to do well.Trent Alexander-Arnold (7/10):Superb assist for Gakpo and defended well for the most part.Joel Matip (7/10):One early slip aside, he was dominant and caused problems when stepping into midfield.Joe Gomez (7/10):Too good for the inexperienced Simms. He and Matip needed this performance.Andy Robertson (7/10):A bundle of energy, and earned major kudos from the home fans when laughing in Pickford's face after a tussle late on.

Liverpool Ratings: Defence

Fabinho (7/10):Much better. Not perfect, but much better. Stefan Bajcetic (9/10):Outstanding. Plays like a veteran, full of confidence and game understanding. A hell of a prospect.Jordan Henderson (7/10):Set the tone with a diligent first-half performance, and helped Liverpool dominate. A big step forward.

Midfield

Mohamed Salah (7/10): Took his goal well, albeit with Pickford's help, and was involved in pretty much everything Liverpool did going forward. Might have had another goal and an assist.Cody Gakpo (8/10):Looked focused and sharp from the word go. Where he needed to be to make it 2-0, and he seemed to grow a few inches thereafter. Direct, strong and quick. This was very encouraging.Darwin Nunez (8/10):Set the tone with his work rate and directness. Caused Everton a ton of problems and set up the opening goal for Salah. Denied one of his own after the break, but played well.

Attack

Diogo Jota (5/10):A welcome return from injury, even if he was understandably rusty.James Milner (6/10):Came on, got stuck in and even found time to break the offside trap.Roberto Firmino (6/10):Another welcome returnee.Harvey Elliott (N/A):On late but still managed to fly into one tackle which had the crowd cheering.Naby Keita (N/A):Late sub.Jurgen Klopp (8/10):Picked the right team and made the right subs. Bench suddenly looks a whole lot stronger.

Subs & Manager

Welcome to Liverpool, Cody Gakpo! Winners, losers and ratings as brilliant Stefan Bajcetic runs Everton ragged in Merseyside derby | Goal.com UK

Liverpool secured the bragging rights in the Merseyside derby against Everton, with Mohamed Salah and Cody Gakpo on the scoresheet, while young Stefan Bajcetic shone in midfield.