Manchester United beat Bolton Wanderers 2-1 to go three points clear in the premier league.
Villarreal went through to the group stage on a 4-2 aggregate crashing Everton's Champions League.
Liverpool came within a point in the battle for third after they drew 0-0 at Aston Villa.
The Man United manager tore a strip off Gary Neville after the England defender was sent off for kicking the ball at Everton fans.
Manchester United beat Everton 2-0 to reach the FA Cup quarter-finals, while 10-man Arsenal were held 1-1 by Sheffield United
Striker Eidur Gudjohnsen scored the winner as Chelsea registered a 1-0 victory over 10-man Everton in the English Premier League.
A review of the weekend action in the leading European leagues.
The England striker's transfer value soared to 50 million pounds following his Euro 2004 performances.
Chelsea romped to a 4-1 home win over Everton in their FA Cup fourth round
Manchester United crushed minor league Burton Albion 5-0 in their FA Cup third-round replay
IMAGES from the English Premier League matches played on Saturday.
Manchester United's Alejandro Garnacho scored with a magical overhead kick in the third minute to send the visitors on their way to a 3-0 victory over an Everton team already reeling in their first Premier League game after being docked 10 points.
Manchester United finished with nine men in a 1-0 defeat at Everton on Wednesday.
The youngest manager in the English premiership, he led Everton to seventh place, their best finish since 1996.
The Manchester United striker finished with one more goals than last season's winner, Thierry Henry.
The club says they have offered their coveted England striker a club record wage of 50,000 pounds a week to stay.
Chelsea forward Diego Costa has been charged for improper conduct following his red card in their 2-0 FA Cup quarter-final defeat by Everton at Goodison Park on Saturday.
Chelsea striker Diego Costa needs to learn to show respect to opponents after the Spaniard goaded Everton players during their pulsating 6-3 English Premier League win on Saturday, Toffees coach Roberto Martinez said.
Sixth-placed United's chances of finishing in the top four were dealt a blow at Goodison Park and the nature of Sunday's defeat prompted manager Ole Gunnar Solskjaer to issue an apology to fans ahead of the clash with their city rivals.
Everton striker Romelu Lukaku struck a late equaliser to salvage a 1-1 draw against a solid CrystalPalace side in an absorbing Premier League match at Goodison Park on Monday.
Images from Saturday's third round matches in the FA Cup.
IMAGES from the EPL matches played on Saturday.
IMAGES from the English Premier League match played between Everton and Manchester City on Wednesday
The London club dominated the first half but fell behind to a superb goal from their former winger Aaron Lennon before young midfielder Dele Alli furthered his case for a place in England's midfield with a classy equaliser just before the break.
Frank Lampard has been tasked with a tough challenge of resurrecting Everton
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.
Images from Saturday's Premier League matches.
A 0-0 Premier League draw against old foes Everton at Goodison Park is not how the Liverpool captain would have dreamt about signing off from the rivals' habitual battle for superiority.
Chelsea took a major step towards the Premier League title with an impressive 3-0 win over Everton at Goodison Park on Sunday.
Images from the English Premier League matches played on Saturday
Liverpool regained their place at the top of the English Premier League with a 2-0 win at Cardiff City on Sunday that restored their two-point lead over Manchester City
Everton have signed winger Gerard Deulofeu from Barcelona on a three-year contract for six million euros ($6.7 million), the Premier League club said on Thursday.
It promises to be a tense and thrilling finale to the season but Liverpool, who have frittered away a seven-point lead, will need to regain their momentum quickly if they are to push for their first league title since 1990.
Wayne Rooney says it is highly unlikely that a scenario would arise causing him to switch allegiances to any Premier League side other than Manchester United or boyhood club Everton in the future.
Images from EPL matches played on Wednesday.
Leicester City's Premier League title defence got off to a terrible start as they were beaten 2-1 at promoted Hull City, who shrugged off an injury crisis to shock the champions on the opening day of the new season on Saturday