Chelsea's fearsome front three stretched Xabi Alonso's perfect start at Stamford Bridge in a thrilling 4-3 win over Brighton on Sunday, while Leeds fought back to hold Brentford 1-1.
Joao Pedro, Morgan Rogers and Cole Palmer scored as Alonso's reign kicked off with a 3-2 win at Fulham on Monday.
Pedro and Palmer were on target once more, while Rogers teed up Chelsea's second goal scored by Pedro Neto as the Blues held off a rally from Brighton that threatened to snatch a point.
Emi Martinez was thrown straight into goal for his Chelsea debut just hours after sealing his move from Aston Villa and became the first player over 30 to start a league game for the Blues in more than two years in the process.
But there was no place for his Argentina teammate Enzo Fernandez, who could still leave for Manchester City before Tuesday's transfer deadline.
Brighton were 4-0 up inside 31 minutes against Villa last weekend, but this time found themselves three goals down in just over half an hour.
Romeo Lavia profited from a mix-up between Bart Verbruggen and Mats Wieffer to prod in the opening goal from a corner.
Neto then turned in Rogers's cross before Pedro rounded off a brilliant Chelsea counter-attack that began inside their own box.
Martinez was beaten moments later by a blistering volley from Malick Yalcouye that brought Brighton back into the game.
Yalcouye was involved again as Pedro turned Pascal Gross's cross into his own net just after the hour mark.
Diego Gomez fired just wide, and Martinez denied Olivier Boscagli an equaliser as Chelsea were suddenly clinging on.
But a moment of genius from Palmer sparked wild celebrations from Alonso as he curled into the bottom corner from outside the box after a solo run across the Brighton defence.
Overlooked by England manager Thomas Tuchel for the World Cup, Palmer has begun the season in top form to give Chelsea hope they could challenge for a first league title since 2016/17.
Gross headed in a stoppage-time consolation for Brighton, but Chelsea join City and Hull as the only two sides to take six points from their opening two games.
LEEDS HOLD BRENTFORD
Brentford were on course to also maintain their perfect start when Kevin Schade's audacious flick opened the scoring away to Leeds.
But Dominic Calvert-Lewin turned in Lukas Nmecha's driven cross to salvage a point and Leeds' unbeaten start to the campaign.
Sunderland got off the mark with a 1-0 victory over Fulham thanks to Wilson Isidor's winner 15 minutes from time.
Manchester United are aiming to bounce back from their opening weekend shocker at Hull against another newly-promoted side, Ipswich, at Old Trafford later.
Marcus Rashford makes his first start for the Red Devils in nearly two years after loan spells at Aston Villa and Barcelona in one of four changes made by Michael Carrick.