Premier League champions Manchester City fell to their first home defeat of the season on Saturday as Ivan Toney secured a shock 2-1 win for Brentford while Tottenham Hotspur recovered from going behind three times to beat Leeds United 4-3.
Liverpool beat Southampton 3-1 as Darwin Nunez scored his first double for the team and Roberto Firmino also got on the scoresheet.
Everton manager Frank Lampard was put under renewed pressure following a 3-0 defeat by Bournemouth while James Maddison scored in a 2-0 win for Leicester City at West Ham United but was then taken off in an injury scare two days after being named in the England squad for the World Cup.
Leicester coach Brendan Rodgers sought to calm fears about the midfielder's fitness, stating he had taken him off as a precautionary measure. Elsewhere, Nottingham Forest beat Crystal Palace 1-0 to move off the bottom of the standings.
Brentford striker Toney, who on Thursday was left out of England's squad for the World Cup, gave the west Londoners the lead in the 16th minute at City and then clinched all three points with a 97th-minute winner after Phil Foden had equalised late in the first half.
"Speaking to some people from the club, this is probably the single biggest ever result, against one of the richest clubs in the world and we have one of the lowest budgets in the division," said Brentford coach Thomas Frank.
City manager Pep Guardiola had no complaints with the result, adding: "The best team won, we struggled from the beginning and we couldn't deal with their long balls."
Tottenham again showed their resilience as well as their appetite for late drama by beating Leeds thanks to goals from Uruguay midfielder Rodrigo Bentancur in the 81st and 83rd minute.
Leeds, who had beaten Bournemouth by a 4-3 scoreline the previous week, took the lead through Crysencio Summerville while Rodrigo Moreno scored twice after Harry Kane and then Ben Davies had pulled Spurs level.
Tottenham coach Antonio Conte had been under pressure following the 2-1 home defeat by Liverpool and the elimination from the League Cup by Nottingham Forest but his side prevailed with their latest stirring comeback, also coming from behind to beat Bournemouth and Olympique de Marseille earlier this month.
"My players showed me big character in this period. In a lot of games we were losing and then we come back. For this reason I think we showed great character, great will to not give up and to believe," said Conte.
Leeds coach Jesse Marsch added: "I'm gutted, I feel like someone has ripped my heart out."
Newcastle United were in action against Chelsea later on Saturday while league leaders Arsenal visit Wolverhampton Wanderers with the chance to increase their advantage over City to five points.
Liverpool's South American strikers Darwin Nunez and Roberto Firmino propelled the team to a 3-1 home win over Southampton in the Premier League on Saturday in their final match before the season pauses for the World Cup.
The victory took Liverpool into sixth place in the league standings on 22 points after 14 matches although Brighton & Hove Albion can climb back above them when they play Aston Villa on Sunday. Southampton are 19th on 12 points after 15 games.
Firmino, who this week was left out of Brazil's squad for the World Cup, put Liverpool in front in the sixth minute by glancing an Andy Robertson free kick into the net.
Moments later Southampton replied with a similar effort, Che Adams rising to head in James Ward-Prowse's set-piece delivery and score the club's first goal under new manager Nathan Jones.
Uruguay international Nunez restored Liverpool's lead in the 21st minute by volleying home a cross from 19-year-old midfielder Harvey Elliot.
The striker, who cost Liverpool a total of 95 million euros when he signed from Benfica in June, grabbed his second goal three minutes before halftime, meeting another cross from Robertson from close range.
Nunez was a handful for Southampton all afternoon, causing chaos in the air every time Liverpool sent a ball into the box and linking up well with his team mates, conjuring up an outrageous backheel to play in Firmino although the Brazilian was thwarted by Southampton keeper Gavin Bazunu.
The second half lacked the frenetic nature of the first although Liverpool goalkeeper Alisson Becker had to make two good saves to preserve his side's two-goal cushion while Mohamed Salah spurned a great chance when he robbed possession and raced free into the area only to miscontrol the ball.
MILNER MILESTONE
James Milner came off the bench to make his 600th Premier League appearance, becoming only the fourth player to do so after Ryan Giggs, Gareth Barry and Frank Lampard."It's a big number isn't it? It's unbelievable. It's been a very long time," said the 36-year-old Milner.
Liverpool defender Trent Alexander-Arnold was pleased his side had been able to build on the momentum from their 2-1 win at Tottenham Hotspur last week, which came after defeats to Nottingham Forest and Leeds United.
"We've had a mixed start to the season, very disappointing results and some good ones. You need consistency in this league and we haven't shown that this season. Last week was a big win and we've followed it up this weekend," he said.
Southampton were playing their first match under Jones, whom the club poached from second-tier Luton Town after sacking Ralph Hasenhuttl following Sunday's 4-1 home loss to Newcastle United, their eighth league defeat of the season.
The visitors showed some fight in the second half but Jones will have plenty of work to do when the season resumes in late December if he is to steer the team away from the relegation zone.
"I saw a young group that showed that they can handle it at somewhere like Anfield. There's a lot of things that I'm really, really pleased with and I learned a lot today," Jones said.
Liverpool coach Juergen Klopp was serving a one-match touchline ban for getting sent off in the win over Manchester City last month but at full-time he came out on to the pitch to salute the home fans.