Kevin de Bruyne struck twice to inspire Manchester City to a dominant 4-2 win at Crystal Palace on Saturday and move the champions level on points with Liverpool at the top of the Premier League table.
Gerard Delofeu's late goal earned Everton a deserved 1-1 draw at Premier League leaders Arsenal on Sunday after Mesut Ozil's strike seemed set to seal three points for the home side.
Vitaliy Mykolenko's 39th-minute own goal had put Luton ahead before Jack Harrison cheered the Everton faithful with an equaliser in the 55th minute, hammering in a low shot that Luton keeper Tim Krul allowed to let slip through his hands.
Troubled AC Milan were held to a goalless draw by AEK Athens
Arsenal claimed their first Premier League win at Everton for six years as Leandro Trossard's second-half strike proved enough to secure the points at Goodison Park on Sunday.
Marouane Fellaini scored late in extra time to spare Everton's blushes as they came from a goal down to beat League One (third division) Stevenage 2-1 and reach the League Cup third round on Wednesday.
Everton now go to up to fifth in the table with 12 points from seven games
Spanish striker Michu hit his fourth goal in three league games but Swansea City missed the chance to top the fledgling Premier League standings after the Welsh side were held 2-2 at home by Sunderland on Saturday.
Erling Haaland's double put Manchester City within touching distance of an unprecedented fourth successive Premier League title
A full-strength Arsenal added another piece of silverware to their recent FA Cup success by beating Everton 3-1 in the final of the Premier League's Asia Trophy on Saturday.
Manchester City and Arsenal closed in on Premier League leaders Liverpool with contrasting victories on Saturday as Manchester United's bubble was burst by Fulham.
IMAGES from UEFA Champions League matches played on Tuesday
IMAGES from the English Premier League matches played on Saturday.
'We always knew it was going to be an important one playing against a quality side, but I think it affected us a little bit too much.
Premier League leaders Manchester City turned on the style with a 3-1 win over Manchester United in their derby clash, on Sunday, leaving Pep Guardiola's unbeaten side two points clear of Liverpool.
Liverpool's new American era began in failure on Sunday in front of their latest owners with a 2-0 loss to Merseyside rivals Everton which sent them second from bottom of the Premier League.
Everton's Romelu Lukaku spared his side a fifth straight defeat by snatching an added-time equaliser to salvage a 1-1 home draw with West Ham United in the FA Cup third round on Tuesday.
Phil Jagielka's stoppage-time thunderbolt earned Everton an unlikely 1-1 draw in the 223rd Merseyside derby on Saturday after Steven Gerrard's free kick appeared to have secured Liverpool a welcome victory.
Phil Foden struck twice as Manchester City stepped up their bid for a fourth Premier League crown in a row with a ruthless 4-0 victory at Brighton & Hove Albion on Thursday.
Manchester City's fingertip hold on their Premier League title was further loosened when a 2-0 loss at Everton followed by runaway leaders Manchester United's 1-0 win over Reading left them praying for a football miracle.
Wayne Rooney's Everton homecoming ended in a 1-0 win over Slovak side Ruzomberok with the former Manchester United striker having a quiet return to Goodison Park in the Europa League, third qualifying round, first-leg on Thursday.
Images from the English Premier League matches played on Saturday.
Everton ended third-tier Oldham Athletic's giantkilling FA Cup run with a 3-1 victory in their fifth round replay on Tuesday to tee up an all Premier League quarter-final against Wigan Athletic.
Jarrod Bowen and Mohammed Kudus' second-half goals gave West Ham a 2-0 win over Manchester United in the Premier League's early game on Saturday, as the Hammers briefly moved into the top six.
The plucky underdogs were brought down to earth as Manchester City, Everton and Stoke City reached the League Cup semi-finals on Tuesday, ending the hopes of second-tier sides who felled fancied opponents in the last round.
Manchester United were humbled 3-0 at home by Newcastle United in the League Cup fourth round
A Romelu Lukaku hat-trick in a 4-1 win for Everton at Young Boys and a thrilling 3-3 draw between Celtic and Inter Milan.
IMAGES from the Premier League matches played in England on Sunday.
News of all that's transpired on and off the football field.
IMAGES from the soccer matches played across leagues on Friday
Chelsea midfielder Cesc Fabregas gave his manager a reminder of his talents by scoring twice in extra time as they fought back from two goals down to knock Premier League champions LeicesterCity out of the League Cup 4-2 on Tuesday.
Ruthless Arsenal threw down the gauntlet in the Premier League title race with a 5-0 thrashing of London rivals Chelsea to roar three points clear at the top of the table on Tuesday.
Manchester United climbed back up to second in the table after second-half goals by Anthony Martial and Jesse Lingard earned a 2-0 victory at Everton -- their first win in five games in all competitions.
Tottenham Hotspur continued their Premier League title push with a 2-0 win over Everton on Wednesday to put them level on points with second-placed champions Manchester United and three behind leaders Manchester City.
Arsenal's victory ended a run of three successive defeats in all competitions and put them level on 43 points with Aston Villa and champions Manchester City. Arsenal's goal difference is superior to Villa's but worse than City's.
Images from Saturday's action in the Premier League.
Wolverhampton Wanderers stunned Tottenham Hotspur 2-1 with stoppage-time goals from Pablo Sarabia and Mario Lemina on Saturday, thwarting the visitors in their bid to reclaim top spot in the Premier League table.
IMAGES from the English Premier League matches played on Saturday
Romelu Lukaku's 50th league goal for Everton put them on the way to a deserved 2-0 victory over West Ham United on Sunday, ending a run of four league games without a win. It kept the Merseysiders sixth in the Premier League and West Ham in the bottom five.
Manchester City rediscovered their swagger to beat Chelsea 2-0 and move into the quarter-finals of the FA Cup on Saturday, Manuel Pellegrini winning the battle of tactical wits against Jose Mourinho.