A rare goal from defender Wes Brown sent Manchester United on their way to a 3-0 home victory over 10-man Liverpool that kept them firmly in charge in the Premier League on Sunday.
Holders Chelsea will meet Liverpool at Stamford Bridge in the quarter-finals of the League Cup next month.
Arsenal regained first place in the Premier League with a 1-1 draw with Liverpool at Anfield.
'Keep Calm And Carry On' could be Claudio Ranieri's motto for the second half of the season after Leicester City earned a 1-0 win at Tottenham Hotspur on Wednesday to put the heat back on Premier League leaders Arsenal.
Liverpool continued their perfect start to the season to stay top of the Premier League after a goal in each half gave them a 2-1 victory over Tottenham Hotspur at Wembley on Saturday.
Arsenal's Olivier Giroud produced a piece of New Year's Day magic to keep Arsenal in sight of Premier League leaders Chelsea while Harry Kane's double bolstered Tottenham Hotspur's ambitions as London's triple assault on the title continues.
'This team is really good and we have invested a lot in it. Now we have to work with that'
Leaders Manchester City were held to a 0-0 draw at Crystal Palace
Holders Chelsea moved into the semi-finals of the English League Cup with a 2-0 victory over Liverpool.
A late mistake by Liverpool goalkeeper Pepe Reina allowed Arsenal to salvage a 1-1 draw at Anfield on Sunday after both sides ended their opening Premier League match of the season with 10 men.
Manchester City suffered their first home Premier League loss in eight months as a shock 3-2 defeat by Crystal Palace on Saturday left Pep Guardiola's champions trailing leaders Liverpool by four points.
Peter Crouch scored a hat-trick as Liverpool thumped Arsenal 4-1 to jump into the third place in EPL.
The result leaves Arsenal in fifth place on 15 points, two behind Leicester City and Chelsea, while Sheffield United moved into ninth on 12 points.
Manchester City moved back into third place and almost guaranteed Champions League qualification thanks to a 3-1 home victory against West Bromwich Albion on Tuesday at the Etihad Stadium.
'I'm very excited to be here. I'm very happy'
Per Mertesacker is confident new goalkeeper Petr Cech will enhance Arsenal's defence and the centre back said he has already developed an understanding with the Czech international.
Manchester City edged past Arsenal and Liverpool beat Chelsea to reach the League Cup semi-finals Tuesday while Cardiff City also made the last four on an emotional night in south Wales.
Arsenal thrashed Middlesbrough 7-0, while Manchester United lost 3-1 at Manchester City in the Premier League.
Manchester United manager Alex Ferguson stuck the boot into Manchester City ahead of their derby clash at Old Trafford on Sunday by insisting that Liverpool will always be United's biggest rivals.
Manchester City defender John Stones headed a controversial stoppage-time winner in a 2-1 victory at Wolverhampton Wanderers on Sunday that took them top of the Premier League and set a club record of 31 league games unbeaten.
The brilliance of Chelsea's Eden Hazard ended Liverpool's 100 percent start to the season as Maurizio Sarri's side enjoyed a 2-1 win at Anfield in the League Cup third round on Wednesday.
League leaders Chelsea and Liverpool however won their matches in the Premier League.
Manchester City came from behind twice to earn a 2-2 draw with Liverpool in a breathless and pulsating Premier League encounter, at Anfield, on Sunday. All four goals came in the second half.
UEFA president Lennart Johansson supports the principle that a club winning the Champions League must be allowed to defend their title.
Juergen Klopp's side returned to English Premier League action on Friday with a hunger and desire that suggested they have spent the close-season break chomping at the bit to get back on the field.
Pepe Reina produced three excellent saves to help lethargic Liverpool earn a point from a goalless and somewhat predictable Premier League draw at Birmingham City on Sunday.
Images from Sunday night's English Premier League matches.
Real Madrid earned their first-ever win over Liverpool with a wondrous Cristiano Ronaldo goal spearheading a 3-0 Champions League victory at Anfield on Wednesday which appeared as classy as it was dominant.
A round-up of Wednesday's action in the UEFA Champions League.
A first-half penalty earned Lille a shock 1-0 home victory over holders Real Madrid in the Champions League group phase on Wednesday.
The striker picked up a hamstring injury in Tuesday's Champions League quarter-final 2-1 defeat by Chelsea.
An opening-day Premier League defeat, a growing injury list and the weight of an unspent transfer kitty hang heavily over Arsenal as they head into Wednesday's Champions League playoff clash with Fenerbahce.
Thierry Henry scored with a brilliant individual effort to give the English side a 1-0 victory in the first leg last 16 knock-out round.
Arsenal's Andrei Arshavin scored four goals in a pulsating 4-4 draw at Anfield on Tuesday to put a huge dent in Liverpool's Premier League title push.
Aaron Ramsey indulged his new goalscoring habit on his return to his boyhood club as Arsenal opened up a seven-point lead at the top of the Premier League with a 3-0 victory at Cardiff City on Saturday.
'I've been here 20 years and many times had the opportunity to leave. I don't have to convince you my preference has always been Arsenal'
Bethany England's early rocket proved enough for Chelsea as they beat newcomers Tottenham Hotspur 1-0.
