Amad Diallo has scored a 90th-minute winner as Manchester United staged a stunning late comeback to beat Manchester City 2-1 in the Premier League.

Four-time defending champions City had led the derby 1-0 going into the 88th minute at Etihad Stadium on Sunday, thanks to Josko Gvardiol's headed goal in the 36th.

But Bruno Fernandes levelled the game from the penalty spot before Diallo flicked the ball past Ederson to score the winner for United.

City fans jeered at the final whistle as their once dominant team's woeful run of form extended to one win and eight losses in 11 games.

It was a first derby victory for new United head coach Ruben Amorim, who led Sporting Lisbon to a 4-1 win against City in one of his last games in charge of the Portuguese club in November.

"I think we did a great job, we controlled it very well," Amorim said.

"We didn't allow much, of course we don't create so much either but it was a divided game. But we believed a lot.

"I think for the fans it has a deep meaning ... but we had a difficult moment one week ago against Nottingham (Forest) at home, in the storm.

"Today is a good day, let's enjoy it for 10 minutes and then think about the next game."

United are now 13th and five points behind fifth-placed City (27 points).

Chelsea won their fourth league game in a row, beating Brentford 2-1 at Stamford Bridge.

Goals by Marc Cucurella and Nicolas Jackson either side of halftime leaves the Blues two points behind leaders Liverpool (36), having played one more game.

Bryan Mbeumo pulled on back in the 90th minute for the Bees, who drop to 11th.

But manager Enzo Maresca continued to insist Chelsea could not win the Premier League title despite moving to within two points of top spot.

"No matter how many games we are going to win, I think we're not ready to compete for the title," said Maresca.

"One of the reasons is I think the team that knows how to compete to win titles will not concede a goal like we concede.

"On 90 minutes, a throw-in for us and we concede a goal. A team that knows how to win titles, that goal they're not to going to concede. It's why I continue to say that we are not ready for titles."

In other games, Tottenham Hotspur eased pressure on manager Ange Postecoglou with a thumping 5-0 home win against bottom-of-the-table Southampton on the south coast.

The former Socceroos boss saw his side score all their goals in a scintillating first half, with Son Heung-Min, Dejan Kulusevski and Pape Matar Sarr on the scoresheet in between a James Maddison double to lift Spurs up to 10th.

The loss prompted Southamption to act swiftly to sack manager Russell Martin as the side remained anchored to the bottom of the league on five points after 16 matches.

"We can confirm that we have taken the difficult decision to part ways with our Men's First Team Manager, Russell Martin," the club said in a statement.

"Going into the start of the season, we all knew the challenges that we would face this year as we readjusted to life in the top flight, competing in the best and most competitive league in the world.

"However, the reality of our situation is clear. The board have supported Russell and his staff and been open and transparent regarding our expectations."

It was a different story for Postecoglou after Spurs claimed their first win in six matches despite being without nine first-team players.

"Look, I said on Friday that nothing changes in me," Postecoglou said.

"I still have the same resolve and determination to make sure that we become the football club and football team we want to be.

"Tonight was about the players and I thought their efforts were unbelievable."

With PA & AAP.