Everton have 36 points from 26 games
Manchester United and Aston Villa paid a heavy price for having men sent off on in the Premier League on Sunday with United losing a tight derby to Man City and Villa surrendering a lead in defeat by Tottenham Hotspur.
Ole Gunnar Solskjaer's side, who had won their last ten away games in the Premier League, stay third on 27 points, a point behind second-placed Leicester.
IMAGES from the English Premier League matches played on Sunday
Jordon Ibe scored a superb equaliser as Liverpool's pre-season tour ended in frustration after they were held to a dull 1-1 draw by a Malaysia XI on Friday.
Southampton's Senegal forward Sadio Mane scored the fastest Premier League hat-trick as he broke a 20-year-old record to help them lead 5-1 at home to Aston Villa by halftime on Saturday.
Liverpool's dream run was demolished in the most unlikely fashion by strugglers Watford on Saturday in what must be considered the most extraordinary reverse of the entire Premier League season. On the evening when the European champions were expected to complete the best sequence in the history of English football's top-flight with a 19th straight league victory, they were instead hammered 3-0 by the team lying one from bottom. Images from the EPL matches played on Saturday.
Aston Villa have sacked manager Tim Sherwood, the Premier League club announced on Sunday.
Images from the English Premier League matches played on Saturday
Images from action in the Spanish Super Cup and English Premier League
Images from the English Premier League matches played on Saturday.
Third-placed Arsenal tightened their grip on a spot in the top four on the English Premier League table, continuing an impressive run of form at the Emirates with a 3-0 win over West Ham United on Saturday.
Manchester City's faltering attempts to retain their title suffered a huge blow on Saturday when they lost 1-0 at Burnley, giving Chelsea the chance to open an eight-point lead when they host Southampton on Sunday.
Juergen Klopp refused to rule out Liverpool as Premier League title contenders on Wednesday after ending the year level on points with Manchester United and nine behind leaders Arsenal.
Steven Gerrard's future at Liverpool may be in doubt but the captain turned back the clock to score in a 3-1 victory at bottom side Leicester City in the Premier League on Tuesday.
Leicester City must wait at least one more day for their first-ever Premier League title after drawing 1-1 with Manchester United at Old Trafford on Sunday.
Images from the English Premier League matches played on Saturday
Imperious Liverpool extended their Premier League home winning streak against Arsenal to six on Saturday with an easy 4-0 victory that lifted them to second in the table.
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.
Images from Saturday's action in the Premier League.
IMAGES from the EPL matches played on Sunday.
Juergen Klopp returns to the scene of one his Liverpool side's most controversial victories of last season this Saturday with the man who fashioned it lining up against him.
Manchester City strengthened their Premier League top-four aspirations with a 5-0 thrashing of a woeful Crystal Palace side at the Etihad Stadium on Saturday.
Manchester United continued their perfect start to the Premier League season by crushing Swansea City 4-0 with three late goals in four minutes.
"It's not much better at the moment. With Daniel's injury we have to take it day by day, and see if he's better," Klopp told a news conference on Friday.
"We want to get back the trust and confidence in our own skills, in our quality. That needs time," he told reporters.
Images from the EPL matches played on Saturday
United manager Louis van Gaal, who had come under scrutiny for sanctioning the deadline-day deal this month and had even been accused of 'panic-buying', was suitably impressed if typically understated.
A goal by Sergio Aguero gave Manchester City a 1-0 victory against neighbours Manchester United, who played with 10 men for more than 50 minutes on Sunday.
Angelo Ogbonna leapt high to power home a header in the dying seconds of extra time to claim a timely first goal for the club as West Ham United sank Liverpool 2-1 on Tuesday to reach the last 16 of the FA Cup.
Philippe Coutinho scored twice as Liverpool recovered from an early deficit to beat struggling Premier League champions Chelsea 3-1 at Stamford Bridge on Saturday and pile more pressure on Blues manager Jose Mourinho.
IMAGES from the English Premier League match played at Selhurst Park in London on Monday
'We were looking at making a positive change -- so Coutinho was going to come off and we were going to put Danny Ings on. I'm glad I kept him on'
IMAGES from English Premier League matches played on Sunday
Chelsea kept up their 100 percent start to the English Premier League season by snatching a 2-1 win at a stubborn Newcastle United on Sunday, grabbing victory thanks to a late own goal by DeAndre Yedlin.
Images from the English Premier League match played between Arsenal and Crystal Palace on Monday
Fans are openly speculating that owner Roman Abramovich, a man who places notoriously high demands on his managers, could call time on Jose Mourinho's second spell at Stamford Bridge if Liverpool can inflict another defeat on the champions.
Chelsea begin their Premier League title defence against Swansea City on Saturday in the unusual position of heading into a new season having been significantly outspent by their rivals.
Soccer highlights from across the globe.
Manchester City beat Swansea 3-1 to make it a perfect 10 victories under Pep Guardiola, including six in the Premier League, as they recorded their best start to a top-flight campaign. City's victory was the perfect riposte to the Spaniard's old rival Jose Mourinho, who earlier saw his remodelled Manchester United sparkle without the dropped Wayne Rooney, thumping Premier League champions Leicester City 4-1. On a day of goals, both Manchester sides were outscored by Liverpool, who crushed Hull City 5-1 to take their tally to 24 in the past eight games.