Reigning champions Manchester City took the lead after 24 seconds but suffered a shock 2-1 defeat at Newcastle United.
In a gripping title race, Liverpool showed they are ready to push Manchester City right until the final seconds of this season with their spirited 3-2 win at Newcastle United.
IMAGES from the English Premier League matches played on Tuesday
Images from the EPL matches played on Sunday
West Ham had lost their first three Premier League games to sit bottom of the table and their dismal start to the campaign had already sparked speculation among pundits as to whether new manager Manuel Pellegrini would see out the season.
Brighton kept a disciplined formation, frustrating Liverpool and as the second half wore on the home side began to lose their fluency.
Five talking-points from the Premier League weekend after Manchester United extended their winning run against Tottenham Hotspur, Liverpool were made to work hard for their win at Brighton & Hove Albion and Arsenal losing at West Ham United.
Liverpool opened up a seven-point gap at the top of the English Premier League with a 1-0 win at Brighton & Hove Albion on Saturday, while Arsenal's poor away form continued with a 1-0 defeat at West Ham United.
Woeful defending led to two Brighton goals in two first-half minutes as 34-year-old Glenn Murray and Shane Duffy outsmarted United's 117 million pound ($149.21 million) back four to demonstrate why manager Jose Mourinho had sought to upgrade it.
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.
Manchester United have scored 14 goals and earned maximum points from their four matches under interim boss Ole Gunnar Solskjaer.
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.
A Roberto Firmino hat-trick proved the highlight of Liverpool's 5-1 demolition of Arsenal as the Premier League leaders opened a nine-point gap over Tottenham Hotspur, who lost 3-1 to Wolverhampton Wanderers.
News of all that's transpired on and off the football field
Five talking-points from the Premier League weekend after Manchester City suffered a shock home loss to Crystal Palace, meaning that Liverpool stayed four points clear at the top following their win over Wolverhampton Wanderers.
IMAGES from the English Premier League matches played on Saturday
Images from the English Premier League matches played on Tuesday
A late goal by substitute Charlie Austin gave relegation-threatened Southampton a thrilling 3-2 victory over Arsenal on Sunday in new Austrian manager Ralph Hasenhuettl's first home game.
Manchester City endured some anxious moments but escaped from fourth-tier Newport County with their FA Cup hopes intact as Phil Foden scored twice in an ultimately comfortable 4-1 fifth-round victory on Saturday.
News of all that's transpired on and off the football field
The midfield duo, who both have dual Moroccan-Belgian nationality, kept Belgium alive with their goals off the bench in the extraordinary round of 16 comeback against Japan and were handed starts in the 2-1 win over Brazil.
Tuesday's semi-final in St Petersburg sees team mates from English champions Manchester City, Chelsea, Manchester United and Tottenham Hotspur go head to head as well as rivalries between club colleagues from Barcelona, Paris St Germain and Monaco.
News of all that's transpired on and off the football field
Real Madrid have signed Spain right-back Alvaro Odriozola from Real Sociedad on a contract until 2024, the European champions said on Thursday.
News of all that's transpired on and off the football field
The home team's record signing Jefferson Lerma, who cost 25 million pounds ($32 million) in August, scored a spectacular own goal to give Arsenal the lead but Norwegian international Josh King, back in the Bournemouth side after injury, equalised just before halftime.
The win moved Spurs up to third but unbeaten Manchester City still looked in a class of their own at the top as Leroy Sane scored twice in a 4-0 stroll over West Ham United.
News of all that's transpired on and off the football field
Mathew Ryan asked his family if anyone wanted to come and watch him play in the World Cup in Russia, there was an enthusiastic response - from 27 of them.
A hat-trick by in-form Scotland midfielder James Forrest earned them a 3-2 home win over Israel in the Nations League and promotion to the competition's second tier on Tuesday.
But it was not all good news for Mourinho, as substitute Marcus Rashford was sent off in the 71st minute for pushing his forehead into Phil Bardsley's head.
Champions Manchester City will expect to get back to winning ways at home to Newcastle United in a match which pits Pep Guardiola against his fellow Spaniard Rafa Benitez.
Liverpool had won each of their previous four home leagues games in which they conceded first and 12 minutes later they had turned another match on its head as Roberto Firmino's trickery set up Mane to give the hosts the lead at the second attempt.
United beat Leicester City at Old Trafford in the opening game of the season but Spurs present a very different quality of opponent.
Egypt have gambled on Mohamed Salah returning to fitness in the coming weeks by naming him in their 23-man squad for this month's World Cup in Russia.
Images from the FA Cup matches played on Saturday
Former Real Madrid striker Predrag Mijatovic criticised Gareth Bale for lacking leadership qualities
Here are five talking points from the weekend's Premier League action:
A round-up of Saturday's matches in the English Premier League.
Tottenham Hotspur's status as Premier League title chasers was seriously harmed on Saturday as they fell to a first defeat in seven league games, losing the lead to go down 3-1 at home to Wolverhampton Wanderers.