Sadio Mane tormented Chelsea as the Liverpool forward struck twice after sparking Andreas Christensen's dismissal in the champions' 2-0 win, while Son Heung-min scored four as Tottenham
crushed Southampton 5-2 on Sunday.
Mane was involved in the turning point at Stamford Bridge as the first clash between Premier League title contenders this season swung Liverpool's way.
In first half stoppage-time, Jordan Henderson picked out Mane's run behind Christensen and the Denmark defender responded by rugby-tackling the Senegal star to the ground.
Mane grabbed his first goal of the season in the 50th minute as he met Roberto Firmino's cross with a thumping header after eluding Reece James' slack marking.
Mane was gifted his second goal as Chelsea keeper Kepa Arrizabalaga made a hash of trying to play out from the back, allowing the Liverpool forward to intercept and slot into the empty net.
It was the latest costly blunder from Kepa, who was dropped twice by Chelsea manager Frank Lampard last season despite his status as the world's most expensive keeper.
Lampard will be relieved that Chelsea are reportedly close to signing Rennes' Senegal international Edouard Mendy as he looks to replace Kepa.
Thiago Alcantara made his Liverpool debut at half-time after his move from Bayern Munich, but the Spain midfielder conceded a 74th minute penalty with a foul on Timo Werner.
Alisson Becker came to Thiago's rescue as he saved Jorginho's spot-kick.
After their chaotic 4-3 win over Leeds on the opening weekend, this was a return to the kind of dominant display Liverpool produced so often en route to their first English title for 30 years last season.
While Chelsea have spent £200 million ($258 million) on new signings in a bid to close the gap on the champions, Liverpool remain streets ahead of the Blues at present.
- Son shines -
At St Mary's, Jose Mourinho hailed Son and Harry Kane after the pair destroyed Southampton.
Just 24 hours after Tottenham signed Gareth Bale, Son delivered a virtuoso display that showed Mourinho's side already have plenty of firepower.
Bale has returned to Tottenham on a season-long loan from Real Madrid seven years after he left the north London club for a then world record £85 million fee.
But the Wales forward will not be available until mid-October as he recovers from a knee injury, so Mourinho needs Son and Kane to carry the attack until then.
Danny Ings put Southampton ahead in the first half, but Son equalised before the break and scored three more in the second half, with each of his goals coming from Kane assists.
Kane, who hit the back of the net twice in the first half only to have them ruled out for offside, capped a swaggering display with his second goal of the season.
"Son was on fire and for me Harry Kane was the man of the match, what he did for the team," Mourinho said.
"With him dropping back and connecting the game between the lines for Sonny to attack, the space they created was a problem they couldn't resolve."
After losing to Everton in their Premier League opener last weekend, Tottenham have lifted the gloom with this vibrant second half performance after the Bale coup.
Neal Maupay's quick-fire double inspired Brighton's 3-0 win against Newcastle as the Seagulls claimed their first Premier League victory of the season.
Graham Potter's side raced into a two-goal lead after just seven minutes at St James' Park thanks to the brace from French striker Maupay.
Aaron Connolly grabbed the third for Brighton, who had Yves Bissouma sent off after his raised boot caught Jamal Lewis in the face.AFP