Manchester City stayed top of the Premier League, second-placed Liverpool also won, Manchester United drew at home and Claudio Ranieri made a winning start at Fulham.
Champions City scored three times in the opening 34 minutes at London Stadium - through David Silva, Raheem Sterling and Leroy Sane, with Sane adding a fourth in injury time - as Pep Guardiola's side cruised to a 4-0 win over West Ham.
Liverpool remain two points behind them after a 3-0 away win at Watford, with Mohamed Salah, Trent Alexander-Arnold and Roberto Firmino scoring, although the Reds ended the match with 10 men after Jordan Henderson was sent off.
Jose Mourinho's Manchester United dropped two points as they could only draw 0-0 at Old Trafford against a Crystal Palace side who have now not won in eight games in all competitions.
- Reaction and analysis from Saturday's Premier League games
- Live: Tottenham v Chelsea
- Brighton 1-1 Leicester City
- Everton 1-0 Cardiff City
- Fulham 3-2 Southampton
- Manchester United 0-0 Crystal Palace
- Watford 0-3 Liverpool
- West Ham 0-4 Manchester City
Ranieri, who won the Premier League title as Leicester manager, was appointed Fulham boss earlier this month and his first match in charge, against Southampton, was a thriller.
Saints went ahead through Stuart Armstrong's goal, Aleksandar Mitrovic equalised and Andre Schurrle made it 2-1 to the London side. Armstrong scored his second to make it 2-2, but a second goal from Mitrovic earned Fulham a 3-2 win, a result that takes them above Huddersfield and off the bottom of the table.
Gylfi Sigurdsson scored the only goal of the game as Everton beat Cardiff City 1-0 at Goodison Park.
Brighton looked on course for three points when Glenn Murray scored and then Leicester City had James Maddison sent off for two bookable offences after only 28 minutes - but the 10 men managed to find an equaliser through Jamie Vardy's penalty as it ended 1-1.
Fourth-placed Tottenham entertain a Chelsea side that are third in the table in the late game (17:30 GMT kick-off).