The draw pushed Chelsea up a place into fourth spot in the Premier League, level on points with third-placed Spurs and one point ahead of Arsenal, both of whom have a played a game less.
Here are five talking points from the weekend's Premier League action:
A preview of the line-up action in the English Premier League.
'It's not easy to handle a team at a big, big club... always demanding to win competitions and every manager needs time. I have the feeling United started to play the way he wants'
IMAGES from the English Premier League matches played on Sunday
IMAGES from the English Premier League match played between Arsenal and Chelsea at Emirates Stadium in London on Sunday.
The ball was in play in Burnley's 2-1 win for just 42 minutes and two seconds out of the regulation 90 minutes.
IMAGES from the English Premier League matches played on Saturday.
Manchester City blew a two-goal lead and had Ederson sent off in a dramatic 3-2 defeat at Wolves on Friday.
United down Newcastle after Saints stun Chelsea on a dramatic night in the English Premier League.
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 the English Premier League matches played on Sunday
Reactions to Liverpool's Premier League triumph, their first league title since 1990:
A preview of the line-up action in the English Premier League.
Swansea went ahead five minutes before the break when an attempt to clear by Liverpool's 75 million pounds ($104.88 million) defender Virgil Van Dijk landed at the feet of Mawson who swept the ball home for his sixth league goal this season.
Images from the English Premier League matches played on Wednesday.
Liverpool's livewire Sadio Mane scored one goal and played a crucial part in the other as they reclaimed the Premier League's top spot with a scrappy 2-1 win at second bottom Fulham on Sunday.
Wes Morgan's 90th-minute header earned 10-man Leicester City a 2-1 victory over relegation-threatened Burnley at Turf Moor in the Premier League on Saturday.
To miss UEFA Super Cup match against Chelsea
A preview of the line-up action in the English Premier League
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.
Liverpool beat Leicester City 2-1 to post a fourth successive Premier League victory but conceded their first goal of the season after a nightmare mistake by new keeper Alisson.
The victory takes Pep Guardiola's side into provisional second spot
Woeful defending led to two Brighton goals in two first-half minutes as 34-year-old Glenn Murray and Shane Duffy outsmarted United's 117 million pound ($149.21 million) back four to demonstrate why manager Jose Mourinho had sought to upgrade it.
There will be no seismic shifts in the balance of the world's richest football competition if the first weekend of the new Premier League season is anything to go by.
After a Champagne Sunday, leaders Chelsea got back to the bread and butter of churning out Premier League points with Eden Hazard's header sealing a 1-0 victory at London rivals West Ham United on Wednesday.
Following is a match by match look at the English Premier League's weekend fixtures
Hazard's dribbling and movement, on and off the ball, constantly posed questions for the Liverpool defence and the winger, who was so central to Chelsea's title triumph last year, certainly looks back up to full speed.
Marcus Rashford scored on his 100th Premier League appearance on Sunday to secure a 1-0 win over Leicester City that kept interim manager Ole Gunnar Solskjaer's dream start going at his old club.
Liverpool opened up an eight-point lead at the top of the Premier League with an emphatic and hugely impressive 3-1 win over defending champions Manchester City.
This time Liverpool are at home, and victory would put them nine points clear.
Third-placed Leicester go to Hodgson's sixth-placed Crystal Palace on Sunday
Liverpool cranked up the pressure on West Ham United manager Slaven Bilic with a 4-1 victory at the London Stadium, while Burnley's remarkable start to the Premier League season continued thanks to a 1-0 victory at Southampton on Saturday.
Leaders Chelsea have seen their lead reduced to just three points after a shock defeat, and a revival from defending champions Manchester City. Manchester United are back in third after a run of five straight wins. If Chelsea slip agains, City continue to pile on the pressure and United keep the winning momentum it will make EPL battle further interesting.
Liverpool head to United with widest gulf in years
Tottenham Hotspur showed the English Premier League title race might not be just a two-horse affair with a hugely impressive 6-2 win at Everton.
A summary of Sunday's Premier League matches
Premier League matches will still be played every weekend over the period, the FA said in a statement http://www.thefa.com/news/2018/jun/08/mid-season-break-confirmed-080618, with five games being held on the first weekend and five on the second.
Juergen Klopp's side, chasing their maiden title in the Premier League era and first in the top flight in 30 years, took a 14th-minute lead from a Virgil van Dijk header but had to wait until stoppage time to put the game to bed through Mohamed Salah.
IMAGES from the English Premier League matches played on Saturday.