Marcus Rashford earned Manchester United all three points with a stoppage time winner at Bournemouthon Saturday.
Bournemouth dominated the first half and took a deserved 11th-minute lead through Callum Wilson -- and after the match Jose Mourinho said he was lucky his side didn't go into half time 6-2 down.
They entered the break at 1-1, with Anthony Martial continuing his good form with the equaliser, and substitute Rashford bundled home in stoppage time after Bournemouth failed to deal with Paul Pogba's cross.
Liverpool remain unbeaten in the Premier League this season but could not hold on for all three points as they drew 1-1 at Arsenal. James Milner gave the Reds the lead in the second half, slamming home inside the box after Bernd Leno failed to hold a cross.
But Arsenal stretched their unbeaten run to 14 matches as Alexandre Lacazette scored a superb equaliser to salvage a point for Unai Emery's men.
Leicester beat Cardiff 1-0 on an emotional day in South Wales. Demarai Gray dedicated his winner to chairman Vichai Srivaddhanaprabha, who tragically passed away following last Saturday's helicopter crash. Gray turned in Ben Chilwell's superb cross and celebrated by revealing a t-shirt with the words: "For Vichai."
Tottenham held on nervously to beat Wolverhampton Wanderers 3-2 away in the Premier League on Saturday after conceding two second-half penalties.
Nuno Espirito Santo's side have now lost three games in a row and slipped to 11th in the standings.
There was a first victory of season for Newcastle at St. James' Park as Ayoze Perez scored the game's only goal against Watford. Ki Sung-yueng drove a free-kick in from the left of the box and Perez headed it past Ben Foster to lift the Magpies out of the relegation zone. Watford's mini run of two consecutive victories came to an end, but they remain in eighth place.
It was not a happy return to the London Stadium for Joe Hart as West Ham beat Burnley 4-2. Marko Arnautovic capitalised on an error by James Tarkowski to give the Hammers a 10th-minute lead. But Burnley improved in the first half and got a deserved equaliser just before the interval when Johann Berg Gudmundsson latched on to Ashley Westwood's through ball to slot past Lukasz Fabianski. However, the visitors couldn't hold on and Felipe Anderson made it 2-1.
Chris Wood looked to have rescued a point when he headed home Gudmundsson's corner to make it 2-2 on 77 minutes, but Anderson put the Hammers back in front six minutes later after turning in the rebound from Arnautovic's shot. Javier Hernandez made it 4-2 in stoppage time when he fired into the top corner.
Everton bounced back from last Sunday's defeat at Old Trafford as Richarlison continued his excellent early season form in a 3-1 victory over Brighton.
The Brazilian finished off a superb conterattack from a Brighton corner to fire the Toffees in front on 25 minutes. But Lewis Dunk equalised for the visitors eight minutes later with their first real attack.
Everton pushed for a second after half-time and re-took the lead when skipper Seamus Coleman scored his first goal in almost two years with a stunning finish from outside the box.
And Richarlison made the points safe when he pounced on Dunk's poor back pass 14 minutes from time.