Chelsea manager Frank Lampard was delighted with the discipline of his team, who ended United's 19-game unbeaten run.
A summary of Saturday's action in the Premier League.
IMAGES from the English Premier League match played between Arsenal and Chelsea at Emirates Stadium in London on Sunday.
Images from the English Premier League matches played on Saturday.
Images from the English Premier League matches played on Saturday.
Chelsea lost their 100 per cent Premier League record when London rivals West Ham United held them to a 0-0 draw on Sunday.
Chelsea's fiery Spain striker Diego Costa snatched a last-minute goal to secure a 2-1 home win over West Ham United and hand new manager Antonio Conte a winning start to his Premier League career on Monday. The bearded Costa collected a header from new signing Michy Batshuayi and thumped it low beyond West Ham goalkeeper Adrian's outstretched right hand to claim the points.
Jota's header earned the three points but it was a struggle in the rain for Juergen Klopp's side who looked uneasy at the back without the injured Virgil van Dijk.
City's Aguero doubtful starter for Watford trip
Images from English Premier League matches played on Sunday.
Images from Wednesday's action in the Champions League.
Images from Monday's action in the Premier League.
Images from the EPL matches played on Sunday
Chelsea's Brazil left back Filipe Luis is poised to return to Atletico Madrid after one season at Chelsea where he failed to hold down a regular first team place, Atletico president Enrique Cerezo said.
Costa, Alba excluded from Spain squad
A flash of attacking brilliance from Olivier Giroud and an emphatic header from substitute Alvaro Morata earned Chelsea a 2-0 win over struggling Southampton
Chelsea midfielder N'Golo Kante was named Player of the Year by the Premier League on Sunday, adding a third individual accolade to a list of achievements this season that includes winning a second consecutive Premier League title.
While Lyon rallied to hold Leipzig 2-2 after a Memphis Depay strike, it was the English clubs who made a mark on the night. Liverpool and Chelsea moved into the last 16 with contrasting wins and now all four English clubs, including Manchester City and Tottenham Hotspur, are in the Champions League knockouts this season.
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.
Gabriel Jesus came off the bench to secure Manchester City a 1-0 English Premier League victory at Leicester City after yet another penalty miss by Pep Guardiola's side on Saturday. Chelsea's Olivier Giroud and Marcos Alonso returned to the starting lineup to stunning effect by grabbing a goal apiece in a crucial 2-1 home win over Tottenham Hotspur in the battle between the London rivals for fourth place.
Here are some of the other events -- in pictures -- that made news last week.
Cesc Fabregas kept alive Chelsea's hopes of finishing in the top four with a quickfire goal in a 1-0 win at Swansea City which leaves the Welsh side facing a major fight to retain their Premier League status.
'He has real technical quality and crucially, pace. But we can't be overly concerned with one player though because they have match winners all over the pitch. We need to nullify them on Wednesday.'
The racist chants took the shine off a great day for Chelsea who have tightened their grip on fourth place.
Chelsea had the look of champions again as they maintained their comfortable seven-point advantage at the top of the Premier League with a 3-1 victory at Bournemouth on Saturday -- but Tottenham Hotspur will not give up the chase.
Premier League-based trio Diego Costa, Juan Mata and Santi Cazorla were among a high-profile list of absentees when Spain coach Vicente Del Bosque named his provisional 25-man squad for Euro 2016 on Tuesday. Costa injured his hamstring against Liverpool in Chelsea's penultimate game of the season. Atletico Madrid striker Fernando Torres was also absent from the squad despite his improved form towards the end of the season, as were Arsenal midfielder Cazorla and Valencia forward Paco Alcacer, Spain's top scorer in their qualifying campaign.
Images from the UEFA Champions League matches played on Tuesday night.
Chelsea could be without Cesc Fabregas and Filipe Luis for clash against Manchester City
Brighton & Hove Albion scored three times in the second half to fight back from two goals down and beat Manchester City
Arsenal right back Hector Bellerin will be in Spain's Euro 2016 squad, the country's football federation said on Tuesday. The 21-year-old Bellerin and the other 18 players named to face South Korea in a friendly in Wals-Siezenheim, Austria on Wednesday, have been guaranteed spots in the European Championship squad. Bellerin was included after Real Madrid right back Dani Carvajal sustained a leg muscle injury in Saturday's Champions League final victory over Atletico Madrid. The Real Madrid and Atletico players in the squad will be named later on Tuesday when Spain coach Vicente del Bosque announces his final list.
Lionel Messi led Barcelona to a 3-1 win at home to Napoli for a 4-2 aggregate victory which took the club into the Champions League quarter-finals, where they face Bayern Munich.
The Professional Footballers' Association (PFA) called for a government inquiry into racism in the English game following the match, which Chelsea won 2-0.
Is VAR sucking the life out of the game?
IMAGES from EPL match played between Manchester City and Chelsea on Sunday
IMAGES from Premier League matches played on Saturday.
News of all that's transpired on and off the football field
Twelve months ago Liverpool were ripping up the record books on the way to their first English top-flight title for 30 years but defeat by Everton on Saturday left them mulling a host of far less flattering statistics.
Alexandre Lacazette's free-kick sent Arsenal into the Europa League semi-finals with a comfortable 1-0 win away over Napoli, while Chelsea beat Slavia Prague 4-3 in a roller-coaster game, helped by a Pedro brace.
IMAGES from the EPL matches played on Sunday
Photos from the Premier League matches played on Sunday