Tottenham Hotspur missed a chance to move clear of relegation danger after Dominic Calvert-Lewin earned Leeds United a 1-1 Premier League draw in North London.
Striker Morgan Rogers netted a double as Aston Villa fought back from a halftime deficit to beat Leeds United 2-1 away.
It was Leeds's first win in four league matches but for West Ham their worst start since 1973-74, when they had the same record after nine games.
Chelsea battled from two goals down to beat West Ham 3-2 in the Premier League on Saturday with a stoppage-time Enzo Fernandez winner.
West Ham United eased the pressure on new manager Julen Lopetegui with a surprise 2-0 victory away to in-form Newcastle United in the Premier League on Monday.
Newcastle United made light work of north-east rivals Sunderland as Alexander Isak's double secured a 3-0 win and a place in the FA Cup fourth round at the Stadium of Light on Saturday.
Wolverhampton Wanderers shared the spoils for the sixth time in 10 Premier League games as Jonny Otto equalised in the second half to earn them a 1-1 draw at Newcastle United on Sunday.
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.
A round-up of Wednesday's action in the UEFA Champions League
IMAGES from Premier League matches played on Saturday.
Manchester City took another decisive step toward an unprecedented fourth successive Premier League title with a 4-0 demolition of Fulham.
The incident was one of many involving match officials being confronted in the top flight at the weekend, with the FA also charging Liverpool manager Juergen Klopp with improper conduct for his outburst at an assistant referee.
Rashford stepped off the bench to fire two late goals to put the seal on an eighth victory in a row in all competitions for the home side.
Rafa Benitez's much-changed side with a youthful streak had looked set to coast through when Sean Longstaff's deflected shot put them ahead after 56 seconds and Callum Roberts volleyed home a second four years since his only other Newcastle appearance.
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 Premier League matches played on Saturday.
Michael Olise scored a stoppage-time penalty as Crystal Palace clawed back from two goals down to draw 2-2 with Manchester City in the Premier League at the Etihad Stadium on Saturday.
A round-up of Sunday night's matches in the Premier League.
The following are talking points from the weekend's Premier League action:
United down Newcastle after Saints stun Chelsea on a dramatic night in the English Premier League.
Images from the Premier League matches played on Saturday.
A summary of the opening day's action in the UEFA Champions league on Tuesday.
IMAGES from the English Premier League matches played on Saturday.
A summary of Wednesday's action in the Premier League.
IMAGES from the English Premier League matches played on Saturday.
Chelsea's third successive league win lifted them level on 18 points with Leicester City but are top thanks to a better goal difference. Leicester face Liverpool on Sunday.
Images from the English Premier League matches played on Tuesday
IMAGES from the English Premier League matches played on Sunday
Tottenham Hotspur missed the chance to move up to provisional fourth place in the Premier League after relegation-threatened Newcastle United held them to a 2-2 draw with a late equaliser from substitute Joe Willock at St James' Park on Sunday. Images from EPL matches played on Sunday.
A summary of Sunday's Premier League matches
Five talking points from the Premier League weekend:
