Southampton and Everton both remain winless and in the bottom three of the Premier League after seeing leads wiped out on Saturday.
Saints seemed destined for their first three points following promotion back to the top flight after 18-year-old Tyler Dibling struck in the fifth minute.
But Russell Martin’s side, who had lost their opening four matches, were unable to hang on and Sam Morsy grabbed an equaliser five minutes into injury time.
Everton also secured their first point in a 1-1 draw with Leicester but will feel it could have been more.
The Toffees led through Iliman Ndiaye’s 12th-minute goal but, in torrential rain at the King Power Stadium, Stephy Mavididi equalised with 17 minutes remaining.
Liverpool returned to winning ways in the league in comprehensive fashion with a 3-0 success against Bournemouth.
In-form Luis Diaz struck twice in three minutes midway through the first half after Antoine Semenyo had an early effort for Bournemouth ruled out for offside, and a fine strike from Darwin Nunez concluded the scoring.
Goals from Nicolas Jackson and Cole Palmer secured a 3-0 away win for Chelsea at West Ham.
Jackson scored twice inside 20 minutes, the first within three minutes of kick-off, and Palmer added a third just moments into the second half on a bad day for new Hammers boss Julen Lopetegui.
Fulham claimed their second league victory of the season, beating Newcastle 3-1.
Raul Jimenez opened the scoring after five minutes and Emile Smith Rowe doubled the lead 17 minutes later.
Harvey Barnes pulled one back just after half-time but Reiss Nelson capitalised on poor defending to make sure of the points in injury time.
It was the same score at Tottenham, where Spurs recovered from conceding a goal inside 30 seconds to beat Brentford 3-1.
The Bees were quick off the mark for the second week in a row, this time Bryan Mbeumo netting, but Dominic Solanke grabbed his first Spurs goal after eight minutes.
Brennan Johnson then put the hosts ahead with 28 minutes gone, his second goal of the week, and James Maddison added the third late on.
Aston Villa also came from behind to defeat neighbours Wolves 3-1 and move level on points with Liverpool and Manchester City at the top of the table.
Matheus Cunha put Wolves ahead in the 25th minute but the momentum swung decisively Villa’s way after Ollie Watkins levelled in the 73rd minute, with Ezri Konsa and Jhon Duran adding further goals.
In the late game, Manchester United were held to a goalless draw by Crystal Palace at Selhurst Park.
Alejandro Garnacho and Bruno Fernandes both hit the bar for United in the first half while goalkeepers Dean Henderson and Andre Onana produced some fine saves.
