Liverpool quickly saw what new recruit Thiago Alcantara can add to their side, while Tottenham's dynamic duo sunk Southampton.
Liverpool ruthlessly capitalised on playing against 10 men in the second half as they eased to victory over Chelsea on Sunday.
The reigning champions have won two from two at the start of the new campaign, as is also the case for Leicester City after they saw off Burnley in the late kick-off.
Brighton and Hove Albion are up and running after a worthwhile journey north, while Tottenham leaned heavily on two of their superstars to put Southampton to the sword.
With help from Opta data, here is a recap of the four fixtures to take place on another busy day in the Premier League.
Chelsea 0-2 Liverpool: Thiago makes debut as champions triumph
A close contest at Stamford Bridge changed complexion when Andreas Christensen was sent off in first-half stoppage time.
Sadio Mane, the player fouled by the defender, went on to score twice after the break, making him just the third Liverpool player to get a brace of goals at Stamford Bridge in the Premier League era. The others? Steve McManaman, back in December 1995, and Philippe Coutinho, who did so in October 2015.
However, the scorer was overshadowed somewhat by new team-mate Thiago Alcantara, who replaced the injured Jordan Henderson at half-time having only completed his move on Friday.
Still, the Spaniard managed to complete more passes (75) than any Chelsea player in the entire match. Indeed, since full passing data became available for the Premier League in the 2003-04 season, his total number of successful passes is the most by a player who featured for a maximum of 45 minutes.
Jorginho missed a penalty for Chelsea too, his first failure in nine attempts for the Blues in all competitions. Alisson not only produced his first save from the spot for Liverpool since joining the club but also his first save of the season.
Southampton 2-5 Tottenham: Bale force! Son and Kane steal the show
Saturday was all about a returning hero for Spurs fans, as the club confirmed Gareth Bale was coming back from Real Madrid on a season-long loan. Less than 24 hours later, Son Heung-min became the headline act for Tottenham, aided by Harry Kane playing a sublime supporting role in a comprehensive win.
Son scored four of his side's goals at St Mary's Stadium. All of them were set up by Kane, who became just the sixth player to assist four goals in a single Premier League game. No Englishman had previously achieved the feat.
To put that into context, Kane – who also scored Spurs' fifth in the rout – only provided two assists in the 2019-20 season, albeit he did miss a large chunk of that due to injury.
All this came after Southampton had taken the lead, though their failure to hold onto the advantage given to them by Danny Ings should hardly be a surprise. Since Ralph Hasenhuttl took charge in December 2018, no side has squandered more points from winning positions in the Premier League.
Still, this was a day to admire the victors, not the vanquished. Son and Kane were simply too much for Southampton; the dynamic duo have now combined for more league goals (24) than any other pairing in the competition since the South Korean joined in August 2015.
Newcastle United 0-3 Brighton and Hove Albion: Seagulls soar thanks to Maupay
What a difference a week makes. Newcastle United were so impressive in their opener at West Ham, while Brighton were well beaten at home by Chelsea. However, the Seagulls' long journey provided plenty of positives, Graham Potter's team running out comfortable winners against accommodating hosts who failed to muster a shot on target.
Neal Maupay had Brighton two ahead inside seven minutes, the earliest brace for a player in the Premier League since Manchester City's Edin Dzeko scored twice in the opening four minutes against Norwich City back in December 2012.
Maupay also set up Aaron Connolly for a third goal late on, with the only disappointment for the visitors the late red card shown to the impressive Yves Bissouma, who had more touches (65) than any other player while also recording a 92 per cent passing accuracy.
Leicester City 4-2 Burnley: Flying Foxes make it two from two
Could history be repeated this term? Leicester have won their first two games of a Premier League season for the first time since their famous title-winning campaign in 2015-16.
For Brendan Rodgers, there was a personal milestone. The Foxes boss recorded his 100th victory in the Premier League, becoming the 23rd different manager to reach a century and needing 210 games. Alex Ferguson (162 games), Kenny Dalglish (197) and Kevin Keegan (209) are the only British managers that did it faster.
James Justin scored his first league goal for Leicester while Harvey Barnes was also on target, meaning he has now been directly involved in five goals in his past three Premier League games against Burnley.
The visitors did not help themselves with Erik Pieters' own goal, Burnley's sixth in the Premier League since the start of the 2018-19 season; the most of any current team in the competition.