Manchester City defeated Salford City in the FA Cup, while Burnley suffered a surprising defeat to Mansfield Town. West Ham United and Norwich City also secured victories in their respective matches.
City, Liverpool all cruise in respective FA Cup matches played on Saturday.
Gabriel Martinelli scored his first hat-trick for Arsenal as the Premier League leaders beat second-tier strugglers Portsmouth 4-1 to reach the FA Cup fourth round.
The commanding scoreline in the cross-town London derby came despite Chelsea's midfield talisman Cole Palmer being ruled out after he felt discomfort on the pitch during the pre-match warmup.
Manchester United plumbed new depths as fourth-tier Grimsby Town knocked them out of the League Cup 12-11 on penalties after a 2-2 draw.
Arsenal's Calafiori secures 1-0 win at Manchester United; Crystal Palace hold Chelsea to 0-0 draw.
Nottingham Forest reached the FA Cup quarter-finals as they beat fellow Premier League club Ipswich Town on penalties after the City Ground clash ended 1-1 after extra time on Monday.
A round-up of Saturday's action in the Premier League.
IMAGES from the English Premier League matches played on Saturday.
Arsenal moved up to second in the Premier League and within six points of Liverpool after a largely trouble-free, if slightly pedestrian, 1-0 win at home to struggling Ipswich Town on a chilly night in north London on Friday.
Images from Saturday's FA Cup quarter-finals.
IMAGES from Premier League matches played on Sunday.
Some lament the FA Cup having lost much of its romance in recent years, in the face of obsession with the Premier League, but this tie had it in bucket loads.
A round-up of Saturday's action in the Premier League.
A round-up of Saturday's action in the Premier League.
Champions Manchester City could only muster a 2-2 Premier League draw with Brighton & Hove Albion on Saturday.
'I want to make as big of an impression as I can and then just try and make the next camp. But obviously, every little kid's dream is to play in a World Cup.'
Three late goals from Amad Diallo dragged a below-par Manchester United to an unlikely 3-1 comeback victory over bottom side Southampton.
IMAGES from the Premier League matches played on Saturday.
Images from Saturday's action in the Premier League.
Welbeck extra-time winner sends Brighton into quarters
A summary of Saturday's action in the FA Cup third round.
A round-up of Tuesday's action in the Premier League.
IMAGES from the Premier League matches played on Sunday
IMAGES from the EPL matches played on Saturday.
A round-up of Saturday's action in the English Premier League.
Manchester United languish 14th in the standings on 19 points, their worst placing to end a calendar year since they were 15th in 1989.
Manchester City thrashed West Ham United 4-1 in the Premier League on Saturday to claim their first back-to-back wins since October.
A round-up of Saturday's action in the English Premier League.
IMAGES from the Premier League matches played on Saturday.
Arsenal were held to a 1-1 Premier League draw by London rivals Fulham on a grey wet Sunday at Craven Cottage as Raul Jimenez scored early for the hosts and William Saliba equalised for the visitors at the start of the second half.
A brilliantly-worked goal by Ryan Christie and a Justin Kluivert penalty gave Bournemouth shock 2-0 Premier League win at home to 10-man Arsenal.
Marcus Rashford and Joshua Zirkzee bagged two goals apiece as Manchester United thumped Everton 4-0 on Sunday in new manager Ruben Amorim's first Premier League match at Old Trafford.
Luton Town knocked out Everton and sixth tier Maidstone United upset Championship Ipswich Town
The favourites to replace Erik ten Hag, who was sacked as Manchester United manager on Monday.
A summary of Saturday's action in the English Premier League.
Liverpool climbed to the top of the Premier League table with a 2-1 victory over struggling Wolverhampton Wanderers on Saturday.
Liverpool strolled to a 2-0 victory over Brentford, while Newcastle drew 1-1 at Bournemouth.
Arsenal closed the gap on leaders Liverpool with a 2-1 Premier League victory at Nottingham Forest
IMAGES from the Premier League matches played in England on Sunday.