Willian's late strike snatched a 1-0 home win for Chelsea over a stubborn Everton side to maintain lead.
The Premier League season is only a week old and the problems are already piling up for misfiring champions Chelsea after a 3-0 thrashing at Manchester City on Sunday.
Manchester City lost 1-0 to Manchester United on Wednesday but hung on to reach the League Cup final 3-2 on aggregate and will face Aston Villa at Wembley. Nemanja Matic's 35th-minute strike gave United victory at the Etihad Stadium but the midfielder was later sent off and it was not enough to overturn the 3-1 deficit from the semi-final first leg at Old Trafford.
Argentina showed once again how reliant they are on Lionel Messi as the Barcelona forward scored a hat-trick in their 4-0 World Cup warm-up win over Haiti on Tuesday.
?The unpredictable nature of the Premier League this season means it is essential for ManchesterCity to beat second-placed Tottenham Hotspur on Sunday to keep their title aspirations alive, right back Bacary Sagna said.
Later on Monday, West Bromwich Albion and Watford were also charged for failing to control their players in Saturday's league game at the Hawthorns, which the hosts won 3-1
AS Roma and Manchester City clash for a place in the last 16 of the Champions League.
Defending champions Manchester City scintillated a stellar performance to record an emphatic 5-0 win over Newcastle, and reduced Chelsea's advantage to five points in the Premier League table on Saturday at Etihad Stadium.
Only one point separates the two sides with Chelsea on 31 and City on 30 but Antonio Conte's impact at Stamford Bridge appears greater than his City counterpart Pep Guardiola's at the Etihad.
Arsenal's victory was scrappy and nervy but Laurent Koscielny's 72nd-minute winner was enough to move them two points clear at the summit after LeicesterCity's surprise push faltered with a goalless draw at home to 10-man Bournemouth.
The visitors' display was enough to earn them applause from their fans at the end.
City salvage draw at home with Sterling's superb late volley after Rooney put Everton ahead. Rooney scored his second goal in as many games this season. The strike was his 200th in the Premier League, making him just the second player after former England forward Alan Shearer to reach that milestone.
Manuel Pellegrini shrugged that he was "not worried about Chelsea" despite seeing his Manchester City team fall further behind the Premier League leaders at the end of a dispiriting week for both the Chilean and his champions.
Manchester City striker Gabriel Jesus failed to find the net in over 700 minutes on the pitch in a run of 10 games between October and November for club and country, as City struggled to keep pace in the Premier League title race and dropped to third. Jesus is City's second-choice striker behind Sergio Aguero and he had admitted to being frustrated earlier this season when Pep Guardiola benched him in favour of the Argentine.
Until this season Manchester City's progression in the Champions League could be measured in baby steps but on Tuesday they can make a huge leap forward when they host Real Madrid in their first European semi-final for 45 years.
Manuel Pellegrini berated referee Mark Clattenburg and said his performance cost Manchester City victory after a breathless 2-2 draw against Arsenal at the Emirates Stadium.
Successive home defeats by leaders Leicester City and second placed Tottenham Hotspur have left City six points off the pace with serious doubts about whether their expensively-assembled squad is still playing for the manager.
Manchester City progressed to the knockout stages of the Champions League from Group F on Tuesday after twice coming from behind to draw 2-2 with Olympique Lyonnais, a team Pep Guardiola hailed as one of the toughest he has ever faced.
ManchesterCity's Ivorian midfielder Yaya Toure said he was the victim of racist abuse from the stands during his side's 2-1 Champions League victory away at CSKA Moscow on Wednesday.
Players from European champions Barcelona made up nearly half of UEFA's Team of the Year which was revealed on Friday, while Cristiano Ronaldo made the lineup for a record 10th time. Eight players from La Liga were included in the final XI, voted for by 7.2 million UEFA.com users from a 40-strong shortlist. Lionel Messi, Dani Alves, Gerard Pique, Andres Iniesta and Neymar were the Barcelona players included, while Real Madrid provided Ronaldo, Sergio Ramos and James Rodriguez.
Leroy Sane struck the winner as Manchester City beat Liverpool 2-1 in a gripping English Premier League clash.
Carlos Tevez has been included in the squad for the first time in three years for next month's friendlies in England against Croatia and Portugal.
Manchester City produced a blistering first-half performance to win 4-1 at Sunderland in the League Cup third round on Tuesday, inflicting more misery on Dick Advocaat's struggling side.
Jose Mourinho's reshaped Manchester United destroyed Premier League champions Leicester City 4-1 with a performance that thrilled Old Trafford on Saturday and justified his decision to leave out Wayne Rooney. The shake-up seemed to liberate Paul Pogba who led the way with a polished display, heading his first goal for the club on 42 minutes and starting the clever move that led to Juan Mata firing home United's second after 37 minutes.
A summary of Tuesday's League Cup matches.
Palermo have rebuffed interest from Manchester United among others for forward Paulo Dybala but could sell the Argentine at the end of the season, president Maurizio Zamparini said on Wednesday.
Pep Guardiola hailed Sergio Aguero's 'unique' skill of sniffing out chances in front of goal, and David Silva's ability to ghost past defenders
Wednesday night saw a few surprise results while a debutant club makes a mark
Images from the EPL matches played on Sunday
Crystal Palace left Manchester City's hopes of retaining their Premier League crown in tatters after a 2-1 win at Selhurst Park on Monday to leave Manuel Pellegrini's side trailing a distant fourth in the title race.
Argentina moved top as South America dominated the monthly FIFA rankings on Thursday with five teams, half of the continent's total, in the top 10.
Ronaldo's nomination comes after the 33-year-old last week denied rape allegations levelled against him by a woman who sued him in court in the United States.
Lionel Messi set a new Champions League scoring record with a hat-trick and Luis Suarez netted his first in Barcelona colours as the Spaniards comprehensively beat APOEL Nicosia 4-0 in the Champions League on Tuesday.
The following is a look back on key moments in the thrilling Premier League title race, won by Manchester City on Sunday:
Liverpool's English Premier League title winning captain Jordan Henderson was named England's Footballer of the Year on Friday in the annual vote of the Football Writers' Association (FWA).
Manchester City survived a late grilling by Real Madrid thanks to goalkeeper Joe Hart to hold on for a 0-0 draw on Tuesday that keeps alive their hopes of reaching the Champions League final for the first time.
Premier League leaders Manchester City recovered from two goals down to beat Championship side Swansea City 3-2 at the Liberty Stadium on Saturday and progress to the FA Cup semi-finals.
Celebration was tinged with disappointment for Manchester City who eased into the Champions League quarter-finals for the first time on Tuesday but lost Vincent Kompany to injury in a 0-0 draw with Dynamo Kiev.
This time Liverpool are at home, and victory would put them nine points clear.
Fernando Torres capitalised on a defensive blunder to score a last-minute winner and secure Chelsea a 2-1 Premier League victory over Manchester City at Stamford Bridge.