West Bromwich Albion inflicted further misery on Manchester United, winning 2-1 at Old Trafford on Saturday to condemn the champions to their worst start to a Premier League season and leave them in the bottom half of the table after six games.
Manchester City boosted their defensive options by signing Argentine centre back Martin Demichelis from Atletico Madrid on Sunday.
Manchester City captain Vincent Kompany is set for a month-long spell on the sidelines after suffering a groin injury in the opening match against Newcastle United, manager Manuel Pellegrini said on Friday.
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.
Images from the EPL matches played on Sunday
Images from the weekend action in the English Premier League.
Images from the English Premier League matches played on Sunday.
Talking points from this weekend's Premier League action as top two Manchester City and Liverpool both won with City remaining a point clear with two games remaining.
Liverpool regained their place at the top of the English Premier League with a 2-0 win at Cardiff City on Sunday that restored their two-point lead over Manchester City
Such is the level of consistency of Manchester City (nine straight wins) and Liverpool (five straight victories), that it can be easy to lose sight of just how good this title race is.
Rewind five years and Liverpool hosted Chelsea with three games remaining, knowing victory would have left them six points clear and a first league title since 1990 almost secure.
Manchester City suffered their first home Premier League loss in eight months as a shock 3-2 defeat by Crystal Palace on Saturday left Pep Guardiola's champions trailing leaders Liverpool by four points.
Second tier Cardiff City beat 10-man Championship rivals Crystal Palace 3-1 on penalties on Tuesday to secure a dream League Cup final date at Wembley with Manchester City or Liverpool.
A preview of the line-up action in the English Premier League
Manchester City suffered a third loss in four matches as Steven Gerrard earned Liverpool a 1-0 victory in the first leg of their League Cup semi-final at the Etihad Stadium Wednesday.
Chelsea brought a whole new dimension to the Premier League title race when they handed Manchester City their first defeat of the season on Saturday to leave Mohamed Salah-inspired Liverpool as the new leaders.
Manchester City overcame a spirited Bournemouth side 3-1 on Saturday to maintain their unbeaten streak and extend their lead at the top of the English Premier League to five points.
English Premier League leaders Liverpool will need to maintain their excellent recent record against Everton in Sunday's Merseyside derby if they are to hold their advantage over second-placed Manchester City.
The 28-year-old's body was flown back to Argentina and arrived in Buenos Aires on Friday morning before being driven the 538 km (334 miles) to Progreso, where he grew up.
Here are five talking points from the weekend's action:
A summary of Saturday's matches in the FA Cup.
News of all that transpired on and off the football field
Norwich City will return to the Premier League next season for the first time since 2005 after clinching promotion Monday.
News of all that's transpired on and off the football field
IMAGES from the EPL matches played on Tuesday
The re-born Paul Pogba scored twice, for the second time since Jose Mourinho's departure from the club, as Manchester United beat Bournemouth 4-1 to make it three wins in a row for caretaker boss Ole Gunnar Solskjaer.
Cardiff had lost six of their previous seven games but, knowing that anything but a victory would probably end their survival hopes after one season in the top flight, overcame a strong Brighton start to play with growing confidence and fully deserved their victory.
United sacked manager Jose Mourinho on Tuesday after the sixth-placed side made their worst start to a season for 28 years.
Manchester City had to battle back from behind to earn a 1-1 draw against Premier League newcomers Wolverhampton Wanderers who gave the champions a real test at Molineux on Saturday.
The Senegal international, 26, joined Liverpool from Southampton in 2016 for 34 million pounds ($43.8 million) and has scored 40 goals in 89 games for the Anfield club.
Tottenham Hotspur have shown impressive durability in the Premier League lately, but they will need to be at their most steadfast to deny champions and league leaders Manchester City who travel to Wembley on Monday.
Newcastle thump Preston in tense match to romp back to the top-tier
Holders and FA Cup favourites Chelsea were handed a home tie against Cardiff City when the fifth-round draw was made on Sunday.
Liverpool continued their perfect start to the season to stay top of the Premier League after a goal in each half gave them a 2-1 victory over Tottenham Hotspur at Wembley on Saturday.
Romelu Lukaku struck twice as Manchester United returned to winning ways after two successive Premier League losses with a 2-0 victory over Burnley at Turf Moor on Sunday.
Goals from Victor Moses and Daniel Sturridge eased Liverpool through a tricky FA Cup fourth round tie at Championship (second division) Bournemouth on Saturday although they had to work hard for a 2-0 victory.
As a baby-faced striker Ole Gunnar Solskjaer made his name coming off the bench to score vital goals for Manchester United and his knack of making a dramatic impact appears undiminished.
Former Manchester United striker Ole Gunnar Solskjaer was named the new manager of English Premier League strugglers Cardiff City on Thursday.
The protracted disagreement between Cardiff City chairman Vincent Tan and manager Malky Mackay reached its inevitable conclusion on Friday when the Scot was sacked seven months after winning promotion to the Premier League.
Cristiano Ronaldo struck twice as a rampant Real Madrid side, featuring the most expensive strike force ever assembled, powered to a 2-0 win over Sevilla in an all-Spanish UEFA Super Cup on Tuesday.