Raheem Sterling scored a hat-trick as champions Manchester City made a convincing start to their title defence with a 5-0 win over West Ham United.
Everton's Theo Walcott struck just after halftime to secure a 1-0 home win over Newcastle United, on Monday, that took the Merseysiders up to eighth in the Premier League, their highest position this season.
Images from the EPL matches played on Saturday
IMAGES from the English Premier League match played between Everton and Manchester City on Wednesday
Images from Saturday's action in the English Premier League.
Manchester United manager Jose Mourinho said his French winger Anthony Martial is finally understanding exactly what is required from him after he delivered an outstanding performance in Sunday's 2-1 Premier League win over Everton.
Belgium and England have already met during the World Cup in a match both teams seemed reluctant to win and on Saturday they will face each other again in a game they both seem reluctant to play. The two sides must pick themselves up and dust themselves down after suffering the crushing disappointment of semi-final defeats to play for the modest prize of third place in a fixture often criticised as pointless.
Images from the English Premier League matches played on Saturday.
England fans are dreaming of World Cup glory after their team banished a decades-long curse of flunking penalty shootouts thanks to a nail-biting win over Colombia.
England turn focus to knockout round and the dreaded penalty shootout
Champions Manchester City have won their last 10 home league matches scoring a total of 36 goals.
England's World Cup 2018 team, and remarkable similarities emerge between the XI expected to start the semi-final against Croatia
It was no surprise that Croatia cavorted on the pitch in celebration with fans and family long after beating England in the semi-finals of the World Cup on Wednesday night, but a wiser head might have ushered them quietly to ice bath and bed.
Twelve months ago Liverpool were ripping up the record books on the way to their first English top-flight title for 30 years but defeat by Everton on Saturday left them mulling a host of far less flattering statistics.
Images from the English Premier League matches on Saturday.
Gareth Southgate's England team has started a new chapter, and rekindled genuine hope.
James Maddison scored a brilliant winner to help Leicester City come from behind and beat Tottenham Hotspur 2-1 in the Premier League on Saturday in a match dominated by VAR drama.
James Rodriguez netted twice and Dominic Calvert-Lewin became the first Everton player to score in the opening four matches of a Premier League season as they beat Brighton & Hove Albion 4-2 on Saturday to stay top of the table with a maximum 12 points.
Premier League leaders Manchester City turned on the style with a 3-1 win over Manchester United in their derby clash, on Sunday, leaving Pep Guardiola's unbeaten side two points clear of Liverpool.
Sergio Aguero proved he is still vital to Manchester City's cause as the Argentine paved the way for a routine 2-0 victory at bottom club Sunderland on Sunday.
IMAGES from the Euro 2020 qualifiers
Manchester United kept up their impressive chase for a top-four spot with a comfortable 3-0 win at relegation-threatened Aston Villa in the English Premier League on Thursday. Relegation-threatened Bournemouth had a late goal disallowed by VAR as they had to settle for a 0-0 draw at home to Tottenham Hotspur.
France earned a rollercoaster 4-2 home win over Croatia in an entertaining top-tier Nations League Group 3 match, while England were held to a 0-0 draw by Denmark in an uninspiring game.
IMAGES from the EPL matches played on Tuesday
A summary of Saturday's matches in the English Premier League.
Troubled AC Milan were held to a goalless draw by AEK Athens
Rodriguez whipped Everton in front from the edge of the box, and Michael Keane and Calvert-Lewin ensured it was two wins from two in the Premier League so far this season.
IMAGES from the English Premier League matches played on Saturday.
Kane takes to world stage as England edge past Tunisia
Virgil van Dijk made a dream start to his Anfield career, scoring the winning goal on his debut for Liverpool, as they beat city rivals Everton 2-1 in a pulsating FA Cup third round tie on Friday.
Liverpool a dramatic 2-1 victory over Leicester City at Anfield, thus maintaining the league leaders' 100 per cent start
Spain began a new era under Luis Enrique in impressive fashion as they came from a goal down to outplay England in a 2-1 win in their Nations League opener at Wembley Stadium on Saturday.
Everton's Romelu Lukaku ended his longest goal drought in English football with an 11-minute hat-trick to power the visitors to an emphatic 3-0 win over Sunderland on Monday and third place in the Premier League table.
Two late goals by Everton substitutes brought the Merseysiders a third successive win when they beat Crystal Palace 2-0 at Goodison Park in Sunday's only Premier League game.
A rejuvenated Manchester United claimed a sixth win from six matches since former striker Ole Gunnar Solskjaer stepped in following the sacking of Jose Mourinho.
Liverpool's livewire Sadio Mane scored one goal and played a crucial part in the other as they reclaimed the Premier League's top spot with a scrappy 2-1 win at second bottom Fulham on Sunday.
Premier League champions Chelsea eased past a disappointing Everton with goals from Spaniards Cesc Fabregas and Alvaro Morata sealing a 2-0 victory on Sunday.
Images from the English Premier League matches played on Wednesday.
'Everton can confirm that Wayne Rooney has rejoined the club from Manchester United on a two-year deal for an undisclosed fee'
Images from the English Premier League matches played on Saturday