Manchester City defeated Salford City in the FA Cup, while Burnley suffered a surprising defeat to Mansfield Town. West Ham United and Norwich City also secured victories in their respective matches.
Chelsea battled from two goals down to beat West Ham 3-2 in the Premier League on Saturday with a stoppage-time Enzo Fernandez winner.
West Ham United bounced back from conceding an early goal to beat Newcastle United 3-1 on Sunday.
Liverpool could be 14th in the table by the time they kick off at West Ham on Sunday afternoon and they will be desperate to steady the ship with three points.
It was Leeds's first win in four league matches but for West Ham their worst start since 1973-74, when they had the same record after nine games.
Manchester United manager Ruben Amorim would have enjoyed some relative calm during the international break after backing from club co-owner Jim Ratcliffe but will find himself in the Premier League maelstrom once again at Liverpool on Sunday.
Erling Haaland took his league tally this season to 11 in eight games with both goals in City's 2-0 home win over Everton -- a result that temporarily put City above Arsenal on goals scored.
Arsenal's Calafiori secures 1-0 win at Manchester United; Crystal Palace hold Chelsea to 0-0 draw.
Newcastle United registered a 2-0 home win over Chelsea on Sunday that moves the Magpies a step closer to Champions League football next season.
Images from the Premier League match between Nottingham Forest and Crystal Palace at Selhurst Park, London, on Monday.
Nuno Espirito Santo's side took the lead after five minutes when a corner fell to Elliot Anderson on the edge of the area and his powerful deflected drive found the net.
City then comfortably closed the game out and victory in their record-extending seventh consecutive FA Cup semi-final means they will face Crystal Palace, who beat Aston Villa 3-0 on Saturday, in the final on May 17.
A round-up of Saturday's action in the English Premier League.
IMAGES from the Premier League matches played on Tuesday.
Champions Manchester City could only muster a 2-2 Premier League draw with Brighton & Hove Albion on Saturday.
Images from Saturday's action in the Premier League.
IMAGES from the Premier League matches played on Saturday.
IMAGES from the Premier League matches played on Tuesday.
Forest were good value for the win, though Ipswich came close to opening the scoring midway through the first half.
A summary of Thursday's action in the Premier League.
IMAGES from the English Premier League matches played on Wednesday.
Round-up of matches from the opening weekend of the English Premier League 2024-25
Arsenal closed the gap on leaders Liverpool with a 2-1 Premier League victory at Nottingham Forest
Third-placed Aston Villa are the surprise package of the season and Unai Emery's side face relegation-threatened Burnley while fifth-placed Spurs host a resurgent Bournemouth who have 19 points from their last seven games.
Images from the English Premier League matches played on Saturday, April 13.
Liverpool moved back to the top of the Premier League with a 2-0 victory at struggling Burnley
Liverpool snatched three points with a wild 1-0 victory over relegation-threatened Nottingham Forest.
Mumbai City FC lost 2-0 to Iranian Club Nassaji Mazandaran in their first AFC Champions League group stage game at home.
Antonio Conte's increasingly fractious relationship with Tottenham Hotspur came to an end with the English Premier League club announcing they had parted ways with the Italian on Sunday.
Nuno's coaching staff have also been relieved of their duties. The club have not yet announced a replacement but British media reported former Chelsea and Inter Milan boss Antonio Conte is linked.
Mason Greenwood's late winner earned Manchester United a 1-0 win at wasteful Wolverhampton Wanderers in the Premier League on Sunday, breaking the record for the longest unbeaten away run in English Football League history in the process.
Tottenham Hotspur have named Antonio Conte as manager until the summer of 2023, the English Premier League club said on Tuesday, a day after sacking Portuguese coach Nuno Espirito Santo.
A summary of the concluding day's action in the Bundesliga, Serie A, Ligue 1 and Saudi Pro League.
Images from Sunday's action in the Premier League.
Manchester City came from behind twice to earn a 2-2 draw with Liverpool in a breathless and pulsating Premier League encounter, at Anfield, on Sunday. All four goals came in the second half.
Manchester City blew a two-goal lead and had Ederson sent off in a dramatic 3-2 defeat at Wolves on Friday.
The result gave West Brom a big boost in their bid to avoid relegation, as they moved to within three points of 17th place, albeit remaining stuck in 19th spot for now. Wolves stay in 14th place.
The paper added that at least four managers as well as players from several teams could be affected.
Manchester City's Pep Guardiola was named Manager of the Year at a League Managers Association awards ceremony on Tuesday after leading his side to the Premier League title and a host of records.
As the Premier League resumes following the international break all eyes will be on Cristiano Ronaldo's homecoming party at Old Trafford on Saturday, with the Portuguese international set to resume his Manchester United career after 12 years away.