Liverpool sent a chilling warning to the rest of the Premier League on Saturday, smashing seven goals past Crystal Palace as Arsenal's crisis deepened following defeat at Everton. Jurgen Klopp's champions -- despite being dogged by injuries this season -- are five points clear of neighbours Everton after humiliating Palace 7-0 at Selhurst Park. It is the first time the Reds have won an away match in the English top flight by a margin of seven goals in their illustrious history. Arsenal, by contrast, are in deep trouble after early-season pacesetters Everton beat them 2-1 at Goodison Park to climb to second in the table, while Manchester City edged past Southampton 1-0. Klopp's men built on the momentum gained from their last-gasp win in the top-of-the-table clash with Tottenham in midweek. Roberto Firmino and Mohamed Salah scored twice while Takumi Minamino, Sadio Mane and Jordan Henderson also found the net. Klopp has repeatedly bemoaned the fixture scheduling that requires teams to play Saturday lunchtime kick-offs after Wednesday evening games, but his side suffered no hangover from their exertions against Spurs. "The boys are capable of that. It will not happen every week but it can happen," said the German. "It just clicked today. After a really intense period for the boys they should be really proud of how they came through that, results-wise." Victory ensured Klopp's side will be top of the league at Christmas for a third successive season and it is difficult to see how they are going to be stopped from winning a record-equalling 20th league title. Salah had been given a rare rest from the start, but his Japanese replacement Minamino opened the scoring in the third minute when he was teed up by Mane for his first Premier League goal. Mane ended his longest goal drought as a Liverpool player -- nine games -- with an excellent turn and low finish from Firmino's pass. Firmino scored twice, either side of a goal from captain Jordan Henderson. Substitute Salah moved to the top of the Premier League goalscoring charts with 13 goals in as many games with a late double, including a spectacular second. Arsenal, without injured forward Pierre-Emerick Aubameyang, show no sign of turning the corner after another painful defeat -- their eighth of a wretched season. Mikel Arteta's team are in 15th place in the Premier League, already 17 points behind Liverpool, but just five points clear of the relegation zone. Everton took the lead in the 22nd minute via a Rob Holding own goal but Nicolas Pepe sent Jordan Pickford the wrong way from the penalty spot for a 35th-minute equaliser. The home side were back in front on the stroke of half-time. Dominic Calvert-Lewin's shot was tipped around the post by Bernd Leno and, from Gylfi Sigurdsson's resulting corner, Yerry Mina rose highest to beat the goalkeeper at his near post. Arsenal, who won the FA Cup in August, have made their worst start to a top-flight season since 1974/75 and face a bleak New Year unless they can find a spark of inspiration from somewhere. "We reacted really well," Arteta told Sky Sports. "We dominated the game. We created enough chances at least to not lose. We hit the bar. We don't have the luck." "The boys are absolutely still fighting," he added. "They're hurt right now." Ancelotti's Everton, on the other hand, have won their past three matches after a wobble. "We are pleased," said the Italian boss. "The position in the table is really good. But as I said last week it is not the end of the season, we have to keep fighting. "But it was a top, top performance today." Manchester City have had an inconsistent start to the season but saw off high-flying Southampton thanks to Raheem Sterling's first-half strike. Struggling Fulham were in action against Newcastle in the late kick-off on Saturday.