Romelu Lukaku's 50th league goal for Everton put them on the way to a deserved 2-0 victory over West Ham United on Sunday, ending a run of four league games without a win. It kept the Merseysiders sixth in the Premier League and West Ham in the bottom five.
An inspired Matteo Darmian scored his first goal for Manchester United and set up another as Louis van Gaal's side kept alive their hopes of a top-four finish with a 2-0 home win over Crystal Palace on Wednesday.
IMAGES from the English Premier League matches played on Tuesday.
Liverpool kicked off the new year three points clear atop the English Premier League standings with a 4-2 victory over Newcastle United.
Spanish striker Michu hit his fourth goal in three league games but Swansea City missed the chance to top the fledgling Premier League standings after the Welsh side were held 2-2 at home by Sunderland on Saturday.
In-form striker Romelu Lukaku said he chose to join Everton on loan for the season from Chelsea because he needed to play regularly and not because he was not wanted at Stamford Bridge.
Arsenal, Everton and Stoke City have all agreed to play in this year's Asia Trophy in Singapore in preparation for the 2015-16 Premier League 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.
Liverpool moved back to the top of the Premier League with a 2-0 victory at struggling Burnley
New Everton boss Sean Dyche's reign began with a shock 1-0 victory over English Premier League leaders Arsenal.
IMAGES from the Premier League matches played on Saturday.
Manchester United were humbled 3-0 at home by Newcastle United in the League Cup fourth round
Gerrard's side turned their fortunes around at the expense of the visitors under Lampard
Chelsea missed the chance to top the table at Christmas when, after having captain John Terry sent off in the 34th minute, their 11-game away English Premier League winning streak ended with a 0-0 draw at Everton on Monday. Terry was shown a straight red for a wild lunge at Leon Osman, taking the steam out of the Londoners, who had dominated until the dismissal but were then forced to hang on in the second half.
IMAGES from the English Premier League matches played on Saturday.
Arsenal missed the chance to take another step towards securing a Champions League place after fellow European hopefuls Everton held firm in a lively 0-0 Premier League draw at the Emirates on Tuesday.
Holders Chelsea needed a late equaliser by Salomon Kalou to snatch a 1-1 draw that kept them in the FA Cup after a Louis Saha header had put Everton on course for a fourth-round upset at Goodison Park on Saturday.
Champions Manchester City slipped to a shock first Premier League defeat of the season at Wolverhampton Wanderers on Saturday, while Manchester United's campaign of woe continued with a loss to Crystal Palace.
Liverpool's new American era began in failure on Sunday in front of their latest owners with a 2-0 loss to Merseyside rivals Everton which sent them second from bottom of the Premier League.
Everton stunned Manchester United 1-0 thanks to a bullet header in the second half by Marouane Fellaini after both teams got their Premier League campaigns underway on Monday.
Images from the English Premier League matches played on Wednesday.
Arsenal exacted revenge against Liverpool on Sunday, Everton kept a dream alive for their manager and Sheffield United caused a dramatic old-fashioned upset as they all reached the FA Cup quarter-finals.
Images from the English Premier League matches played on Tuesday.
Fellow Serie A sides Atalanta and Lazio also won while Portugal's Vitoria Guimaraes began their match against Salzburg with not a single European player in the team.
Marouane Fellaini scored late in extra time to spare Everton's blushes as they came from a goal down to beat League One (third division) Stevenage 2-1 and reach the League Cup third round on Wednesday.
Manchester City roared back to the top of the Premier League with a 6-1 thrashing of Bournemouth after Manchester United steadied the ship
Everton's teenage striker James Vaughan may return for the club's run-in to the season despite severing an artery in his foot on Monday.
Chelsea banished any fears of a repeat of last season's shock FA Cup fourth-round exit to Bradford City when they crushed Championship (second-tier) side Milton Keynes Dons 5-1 away to reach the fifth round on Sunday.
A stoppage-time goal from Martin de Roon earned Middlesbrough an unlikely 1-1 draw at Premier League leaders Manchester City on Saturday.
"In this period, everyone's thinking of New Year's Eve, the distraction can be a problem. Two days after Leeds, we have to be ready."
Images from Saturday's action in the Premier League.
Rafael van der Vaart's speculative long shot just before halftime sent Tottenham Hotspur into the FA Cup fifth round with a fortunate 1-0 win at Watford on Friday.
The European champions are likely to play CSKA Sofia in the Champions League third qualifying round.
Just as the umpire's decision is no longer final, what is disdainfully rejected is the age-old dictum that the game should be played and watched in the spirit of the game, sighs Uddalok Bhattacharya.
Manchester City's fingertip hold on their Premier League title was further loosened when a 2-0 loss at Everton followed by runaway leaders Manchester United's 1-0 win over Reading left them praying for a football miracle.
The race for Premier League places in next season's Europa League warmed up on Sunday when Aston Villa and Everton fought out a thrilling 3-3 draw and Fulham came from behind to win 3-1 at Manchester City.
Kyle Walker extends Manchester City stay until 2026
Manchester City went top of the Premier League, at least until Manchester United play at Stoke City later on Saturday, when they beat Everton 2-0 at the Etihad Stadium with goals from second-half substitutes Mario Balotelli and James Milner.
IMAGES from the English Premier League matches played on Saturday.
Manchester City's Argentina striker Carlos Tevez scored a hat-trick two days after he was arrested as they cruised past Barnsley 5-0 to join history makers Wigan Athletic in the FA Cup semi-finals on Saturday.