Raheem Sterling scored a stunning 96th-minute winner as Manchester City dramatically edged Southampton 2-1 on Wednesday to preserve their eight-point lead at the Premier League summit.

Pep Guardiola's side looked set to drop points after Oriol Romeu cancelled out Kevin De Bruyne's opener, only for Sterling to give City a 19th straight win in all competitions and a club-record 12th successive win in the league.

It was Sterling's third late winner in as many games and will have sickened second-place Manchester United, who had closed to within five points of the leaders by winning 4-2 at Watford on Tuesday.

"It was an astonishing end to the game. It means a lot," City manager Guardiola told the BBC.

"What happened in the locker room was amazing. We want to win the league, but you have to celebrate when you score in the last breath like that."

Elsewhere there were wins for Chelsea, Arsenal, Liverpool and upwardly mobile Burnley, while Wayne Rooney scored a hat-trick as Everton beat West Ham United 4-0 in front of Sam Allardyce, who is set to become their new manager.

Everton remain the last team to have avoided defeat against City, having drawn 1-1 at the Etihad Stadium in August, although Wolverhampton Wanderers took them to penalties in the League Cup.

City went ahead in the 47th minute against Southampton when Virgil van Dijk, under pressure from Nicolas Otamendi, diverted De Bruyne's free-kick into his own net, with the Belgian midfielder awarded the goal.

Romeu levelled with 15 minutes to play when Sofiane Boufal helped the ball into his path and the Southampton midfielder hammered a shot in off the crossbar.

But with time almost up, Sterling exchanged passes with De Bruyne and curled a glorious shot past Fraser Forster to send Guardiola into raptures on the touchline.

Third-place Chelsea belied the first-half dismissal of manager Antonio Conte for dissent to win 1-0 at home to Swansea City courtesy of a 55th-minute header by defender Antonio Rudiger.

"The problem is I was frustrated because the opponents were wasting time," explained Conte.

"But I have apologised because I did the wrong thing."

Mesut Ozil shone on his return to Arsenal's starting XI after illness as Arsene Wenger's men thrashed Huddersfield Town 5-0 to tighten their grip on fourth place.

Alexandre Lacazette set Arsenal on their way to a 12th straight home league win by finishing from Aaron Ramsey's flick in the third minute.

- Salah double -

Ozil put the game to bed in a dazzling four-minute spell mid-way through the second half, setting up goals for substitute Olivier Giroud and Alexis Sanchez before finding the net himself. Giroud completed the scoring.

Liverpool leapfrogged Tottenham Hotspur into fifth place courtesy of a 3-0 victory at Stoke City.

Jurgen Klopp's side took the lead through Sadio Mane's neat dink in the 17th minute and substitute Mohamed Salah added a late brace, the first of which was a stunning volley, to take his goal tally for the campaign to 12.

Burnley also crept above Spurs after Robbie Brady made a goal for Chris Wood and scored one for himself in a 2-1 win at Bournemouth, who replied through Josh King.

Man of the day was the evergreen Rooney, who scored his first hat-trick in over six years to lead Everton to a morale-boosting win over third-bottom West Ham.

Allardyce was in the stands at Goodison Park after Everton announced he was finalising terms to succeed the sacked Ronald Koeman as manager.

David Moyes returned to Goodison as West Ham manager and had the misfortune to have a front-row seat for a sensational performance by the player whose career he launched.

With David Unsworth still in caretaker charge, Everton took an 18th-minute lead when Rooney headed in at the second attempt after his penalty was parried by Joe Hart.

Tom Davies teed up Rooney to sweep in a second and after Everton goalkeeper Jordan Pickford had saved a spot-kick from Manuel Lanzini, Rooney completed his hat-trick with a stupendous goal.

After racing from his box, Hart fluffed his clearance and from 15 yards inside his own half, Rooney drilled an exquisite first-time finish back over the West Ham goalkeeper's head.

Ashley Williams added a late fourth to complete Everton's second win in 13 matches.

"Great hat-trick, great display from Wayne," said Unsworth, who revealed he had spoken to Allardyce before the game.

"I'm delighted for the club. I took over when we were in the bottom three and we've got out of it in the six weeks."