Manchester United's nightmare winless run reached nine games as they slid to a 2-0 loss at Chelsea and Manchester City also suffered a harrowing Halloween as the Premier League leaders went down 1-0 at home to Brighton & Hove Albion on Saturday.

United were the better team before halftime at Stamford Bridge but paid heavily for not taking chances as a solo effort by Morgan Rogers and a Cole Palmer penalty after the break heaped more pressure on the visitors' manager Michael Carrick.

A horror start to the second half for Carrick's side was compounded by a needless red card for defender Lisandro Martinez in conceding the penalty that Palmer tucked away in the 64th minute.

United were spared dropping into the relegation zone by Nottingham Forest's 2-0 defeat at Brentford although they will fall into the bottom three should Crystal Palace earn at least a point at Tottenham Hotspur later.

City's 100% Premier League record was ended last week by Aston Villa and their hopes of bouncing back quickly were undone by third-placed Brighton who avenged their midweek League Cup loss to City thanks to Yasin Ayari's early goal.

Champions Arsenal will replace City as leaders if they avoid defeat at Liverpool on Sunday. City have 21 points from nine games with Arsenal also on 21 from eight with Brighton on 19.

Coventry City moved out of the relegation zone with a 3-1 home win over Sunderland who are left propping up the table.

Bournemouth beat Leeds United 2-0 to move seventh while Forest remained in the bottom three as their poor form under new manager Oliver Glasner continued with defeat at Brentford making it five league games without a win.

The battle between two of the promoted sides ended honours even as Hull City drew 2-2 at home to Ipswich Town.

Carrick has now overseen United's longest winless run since 1988 and a fourth successive Premier League defeat means they have just seven points from their opening nine games.

Despite the stark statistics, Carrick was warmly applauded by the travelling fans after the final whistle.

Bruno Fernandes returned to the starting line-up as captain after being benched for last week's defeat at Bournemouth for his critical comments aimed at Carrick, and United were rejuvenated as they enjoyed the better of the first half.

Things could have been so different had Matheus Cunha's goal been allowed to stand or a host of opportunities been taken, including Amad firing over when he looked odds on to score.

All United's good work unravelled after the break, however, with Martinez, who also criticised the club's hierarchy, the villain.

He allowed Rogers to stroll through unopposed before dinking Chelsea's opener and received two yellow cards in three minutes, the second for inexplicably pushing his arm into the face of Wesley Fofana at a corner to concede a penalty.

"I think I take away a lot of the positives from the first half," Carrick said.

"But the game unravelled and got away from us. It's happened too often really so we've got to learn from that and we've got to do something about it pretty quickly."

City had done an impressive job of ignoring the dark clouds hanging over the club after an independent commission found them guilty of 114 out of 115 financial charges but after winning their opening seven Premier League games, Enzo Maresca's side have suddenly hit the buffers.

They fell behind in the 11th minute when a miscued clearance by Matheus Nunes fell for Ayari who converted from close range.

City poured on the pressure in search of an equaliser but Brighton, who had led twice against City in the League Cup, produced a textbook away display to hang on to the points.

The hosts had 21 goal attempts but failed to score for the first time in 25 Premier League matches.

Fabian Hurzeler's Brighton side have now beaten Arsenal and City this season and while they have been free-scoring, they showed another side at City.

"There's an old phrase -- defence wins you battles and wins you championships. Of course, we're not speaking about the championship, but especially today we needed to have this defensive mindset. It's always a togetherness when you defend like we did," Hurzeler said.