Bukayo Saka scored either side of halftime as Arsenal crushed second-bottom Burnley 5-0.
Roberto Firmino's 90th-minute header sent Liverpool back to the top of the Premier League with a 2-1 victory over Tottenham Hotspur, whose 11-match unbeaten run came to an end on Wednesday.
Headers by Romelu Lukaku and Nemanja Matic earned Manchester United an unconvincing 2-0 victory over Brighton and Hove Albion in a low-key FA Cup quarter-final played in freezing conditions on Saturday.
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.
Although Spurs always looked more comfortable on the ball it was Sean Dyche's side, who have just a point from their opening five games, who had come the closest.
News of all that's transpired on and off the football field
The price eclipsed the A$425,000 achieved by the late Don Bradman's baggy green when it was sold in 2003.
Here are five talking points from the weekend's action:
Manchester United remain winless at home in the league this season after Arsenal enjoyed their first win at Old Trafford
Liam Delap, the son of former Stoke City defender Rory, scored the opener for Pep Guardiola's side in the 2-1 win at the Etihad Stadium
Brighton kept a disciplined formation, frustrating Liverpool and as the second half wore on the home side began to lose their fluency.
A night of wholesale team changes for the 11 Premier League sides in action produced one notable upset with top flight Stoke City losing 2-0 at second-tier Bristol City.
Bayern Munich wasted a two-goal lead and needed a lucky 82nd- minute winner from Joshua Kimmich to beat Borussia Dortmund 3-2 in Germany's Super Cup on Wednesday and secure their fifth title of the year.
Images from Saturday's action in the English Premier League.
Bernardo Silva has made an encouraging start to the Premier League campaign and the Manchester City midfielder said that feeling more settled at his second season with the champions was a key factor in his performances.
Liverpool face Spurs in the game of the weekend, a day after title rivals Manchester City travel to struggling Fulham.
A round-up of Saturday's action in the Premier League.
Romelu Lukaku extended his impressive FA Cup scoring record by netting twice in Manchester United's 2-0 win at Huddersfield Town to earn Jose Mourinho's side a quarter-final tie at home to Brighton & Hove Albion.
Liverpool head to United with widest gulf in years
Images from Sunday's action in the Premier League.
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.
IMAGES from Premier League matches played on Saturday.
Liverpool manager Brendan Rodgers was an immensely proud but competitive dad at Anfield on Sunday as his Premier League side overcame the FA Cup challenge of his son's third tier Oldham Athletic.
Images from Sunday's English Premier League matches.
Arsenal's best chance to equalise came from a Granit Xhaka free kick which looked destined for the top corner until the Gunner's former keeper Emiliano Martinez at full stretch pushed it around the post with a fingertip save.
Under-fire Jose Mourinho had been on the verge of delivering the perfect response to his critics on Saturday with Manchester United closing in on a second consecutive comeback win, at the home of his old club Chelsea to boot.
A round-up of the action in the English Premier League on Monday.
Ayew strikes as Palace hold Southampton to 2-2 draw
Manchester City's Sergio Aguero had said a number of players would be fearful of resuming the season amid the virus outbreak with more than 4.02 million people infected globally and over 276,000 dead.
News of all that's transpired on and off the football field
Talking points from this weekend's Premier League action as top two Manchester City and Liverpool both won with City remaining a point clear with two games remaining.
Valencia sign Kondogbia on loan from Inter
A preview of the line-up action in the English Premier League
Spain are still favourites to finish top of Group E above Sweden, Poland and Slovakia but, after struggling to break down conservative sides such as Georgia and Greece in March, they know coming first will not be a procession.
Manchester City needed a second-half penalty from striker Erling Haaland to break the resistance of a dogged Crystal Palace.
Chelsea moved into the Premier League's top four as Mason Mount's superb first-half goal earned them a 1-0 win at champions Liverpool who suffered a club-record fifth straight home league defeat on Thursday.
Spurs striker Bergwijn is major casualty as Netherlands trim squad
Manchester City host Tottenham Hotspur on Saturday on the back of a record 15 successive English Premier League wins, and on the basis of their visitors' recent away form, a 16th victory appears to be the likely outcome.
Following is a match by match look at the English Premier League's weekend fixtures:
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.
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