Liverpool started the ball rolling with a convincing 4-1 win at home to promoted Norwich and City responded a day later with an even more emphatic 5-0 victory at West Ham United.
Here are six who could make the biggest impact in this season's English Premier League.
News of all that's transpired on and off the football field
United looked dead and buried as they struggled to get back into the contest after the break but 19-year-old Brandon Williams's first senior goal 18 minutes from time sparked them into life. However, substitute McBurnie denied the visitors in stoppage time to add a further twist to the breathless encounter, squeezing a strike past De Gea, with the goal awarded after a lengthy VAR review.
It was a third successive 0-0 draw for United after a stalemate at Chelsea on Sunday and against Real Sociedad last Thursday which completed a 4-0 aggregate win over the Spanish side in the Europa League.
Images from UEFA Europa League semi-finals played on Thursday.
A video of the incident showed that Taison stuck his finger up at a section occupied by Dynamo fans and then hoofed the ball into the stands.
Manchester United, Sevilla and Celtic led a parade of clubs with continental pedigree to book the first places in this season's Europa League knockout stage.
A round-up of Sunday night's matches in the Premier League.
City have 89 points, one more than rivals Liverpool, with both teams having three games to play -- and none of them against top six opponents.
Messi, whose deal expires in 2021, had called his side "weak" and "inconsistent" after they lost the league title to Real Madrid.
Liverpool took a giant step towards their first title since 1990 on Saturday when their 3-0 win at Bournemouth combined with Manchester United's 2-1 victory at Manchester City to leave the champions 14 points adrift of the Premier League leaders.
IMAGES from the English Premier League matches played on Sunday.
Images from the UEFA Champions League matches played on Tuesday night.
IMAGES from the EPL matches played on Wednesday
Spanish playmaker Mata, 31, joined United in 2014 for a then club record transfer fee of 37.1 million pounds ($46.86 million) from league rivals Chelsea.
A KrisCommons header gave former European champions Celtic a 1-0 win over Swedish side Elfsborg Boras while Fenerbahce made the most of their Champions League lifeline with a 1-1 draw against Salzburg in the first leg of their third qualifying round tie on Wednesday.
News of all that transpired on and off the football field.
Ousmane Dembele struck early and Lionel Messi converted a late penalty as Barcelona won 2-0 at Juventus in the Champions League on Wednesday after Alvaro Morata had three goals disallowed for offside for the Serie A side.
Images from the English Premier League matches played on Sunday.
Manchester United have signed Leicester City's England centre back Harry Maguire on a six-year contract, the Manchester club announced on Monday.
Manchester United beat AC Milan 5-4 on penalties after their International Champions Cup match in Cardiff's Millennium Stadium ended 2-2 in regulation time on Saturday.
Bruno Fernandes and Edinson Cavani scored twice each as Manchester United took a giant step towards the Europa League final with a 6-2 drubbing of AS Roma in their semi-final first leg at Old Trafford on Thursday.
News of all that's transpired on and off the football field.
News of all that transpired on and off the football field
News of all that's transpired on and off the football field
Second half goals from Presnel Kimpembe and Kylian Mbappe gave the impressive French side a clear advantage ahead of the return in Paris on March 6.
Five talking-points from the Premier League weekend after Manchester United extended their winning run against Tottenham Hotspur, Liverpool were made to work hard for their win at Brighton & Hove Albion and Arsenal losing at West Ham United.
Yuvraj Singh said he has been following Manchester United for more than 20 years
Salah back in Liverpool squad but may not be risked at Genk, says Klopp
Four-time European Champions Ajax Amsterdam were felled at the first hurdle of the continent's second tier Europa League on Thursday, exiting in the group stage two days after rivals PSV Eindhoven celebrated long-awaited success.
News of all that's transpired on and off the football field.
On a crazy evening it looked as though Joe Willock's screamer had earned Arsenal a memorable victory, but Liverpool proved irrepressible as their barnstorming season continued.
IMAGES from the English Premier League matches played on Tuesday
News of all that's transpired on and off the football field
News of all that's transpired on and off the football field
Manchester United kept up their impressive chase for a top-four spot with a comfortable 3-0 win at relegation-threatened Aston Villa in the English Premier League on Thursday. Relegation-threatened Bournemouth had a late goal disallowed by VAR as they had to settle for a 0-0 draw at home to Tottenham Hotspur.
Images from the UEFA Champions League quarter-final first leg matches played on Wednesday
The Professional Footballers' Association (PFA) called for a government inquiry into racism in the English game following the match, which Chelsea won 2-0.
Images from Sunday's action in the Premier League.