Sixteen-year-old Rio Ngumoha scored a sensational late winner as Liverpool overcame 10-man Newcastle 3-2, while fellow title challengers Arsenal thrashed Leeds 5-0 on home turf.
Manchester City, however, suffered a 2-0 defeat at the hands of Tottenham and Chelsea dealt further damage to West Ham with a 5-1 hammering on their travels.
Elswehere, Everton won the first Premier League game at their new stadium, beating Brighton 2-0 and there were wins for Bournemouth, Brentford and Burnley.
Here is Flashscore's Team of the Week, based on our player ratings system.
Goalkeeper
Jordan Pickford (Everton) - 8.2
Jordan Pickford proved exactly why he is England's number one as he backstopped Everton's win over Brighton in their first competitive game at their new stadium.
The 31-year-old made four saves for the Toffees, with his best coming from the penalty spot as he blocked Danny Welbeck's spot kick to deny Brighton a route back into the game.
Defence
Jurrien Timber (Arsenal) - 10
It was a superb day for Jurrien Timber as he marked Arsenal's thumping win over Leeds with two goals, an assist and a clean sheet.
The Dutchman headed in his first well, before teeing up Bukayo Saka and prodding in his second to confirm the rout for the Gunners.
Timber is the first player in the Premier League this season to earn a perfect Flashscore rating of 10.
Trevoh Chalobah (Chelsea) - 8.5
Trevoh Chalobah had a good evening at both ends of the pitch as Chelsea battered Graham Potter's West Ham.
Chalobah won both his tackles and made three clearances, while he was rewarded for his efforts by scoring the Blues' fifth goal from close range.
Riccardo Calafiori (Arsenal) - 8.3
Arsenal's other full-back Riccardo Calafiori also did well against Leeds, getting up and down the left flank when required.
His searching pass down the wing led to Viktor Gyokeres' first Arsenal goal, while he coped with his defensive duties.
James Garner (Everton) - 8.5
Filling in at left-back, James Garner hardly looked out of place as he battled against Brighton's tricky forwards.
His hard work was crowned with a wonderful driven goal from distance in front of Everton's towering south stand, which earned him a rousing reception.
Garner also came away with nine clearances and two key passes to reassure David Moyes of his decision.
Midfield
Iliman Ndiaye (Everton) - 8.5
Iliman Ndiaye followed up his Goodison Park-closing goal with the first at Hill Dickinson Stadium to really cement his name in Everton history.
The Senegalese looked lively throughout against Brighton and finished off a good move following some great work from the rejuvenated Jack Grealish.
Josh Cullen (Burnley) - 8.3
Burnley captain Josh Cullen led by example to aid the Clarets towards their first points of the season as they beat fellow promoted side Sunderland 2-0.
Cullen scored the opener with a well-placed finish into the corner and his teasing ball in behind set away Jaidon Anthony to seal the victory.
Joao Pedro (Chelsea) - 9.2
Joao Pedro dropped into an attacking midfield role following Cole Palmer's pre-game injury, and he never looked back as he produced a fine performance.
The Brazilian scored Chelsea's opener with a fine header and notched the assists for Pedro Neto and Chalobah's strikes later in the game.
Pedro won a game-high nine duels and created two big chances in a ruthless display from Enzo Maresca's team.
Marcus Tavernier (Bournemouth) - 8.0
An industrious showing from Marcus Tavernier guided Bournemouth towards their first win of the campaign as they defeated Wolves 1-0 at home.
Tavernier recorded the lone goal of the game in the fourth minute when his strike took a wicked deflection and found its way into the net via the crossbar.
Forwards
Bukayo Saka (Arsenal) - 8.2
Bukayo Saka got his scoring going for the season with a well-taken goal from a tight angle to double Arsenal's advantage against Leeds.
Saka created two chances in the game before he was forced to be withdrawn with a hamstring injury early in the second half.
Viktor Gyokeres (Arsenal) - 7.9
Off the mark for Arsenal, Viktor Gyokeres will be hoping the goals will start to flow after his double in the Leeds battering.
The Sweden striker took his first well after cutting in and finishing low from the left and smashed in a late penalty to cap off Arsenal's five-star showing.
