Liverpool continued their 100% start to the season with a win at Aston Villa, while Arsenal bounced back from opening day defeat by cruising to victory against Fulham at Craven Cottage.
Stoke completed a dramatic turnaround at the Britannia Stadium to defeat Crystal Palace, Hull City held on against Norwich to claim their first points on their return to the top flight, Southampton scored a late equaliser to deny Sunderland all three points at St Mary's, while Everton and Newcastle both ended with goalless draws against West Brom and West Ham respectively.
Liverpool joined Chelsea at the top of the table with a hard-fought 1-0 win over a battling Aston Villa side at Villa Park.
Daniel Sturridge jinked his way through the home side's defence midway through the first half before poking the ball into the roof of the net from close range to notch the only goal of the game - and the England striker's eighth goal in his last seven league games.
Villa improved in the second half and Christian Benteke twice tested Simon Mignolet, while both sides had penalty appeals waved away late in the game.
Lukas Podolski netted a brace as Arsenal defeated Fulham 3-1 in their London derby at Craven Cottage.
Olivier Giroud struck his third goal in as many games to give Arsenal the lead after 14 minutes, getting onto the end of an Aaron Ramsey shot and neatly lifting the ball over David Stockdale in the Fulham goal.
Podolski then doubled the advantage four minutes before half-time, powerfully side-footing the ball into the roof of the net after Stockdale denied Walcott.
Midway through the second half, Podolski fired in his second of the game to put Arsenal into a comfortable position. Darren Bent came off the bench to net on his Fulham debut, but it proved to be no more than a consolation.
Stoke City scored twice in four minutes to see off Crystal Palace 2-1 in a dramatic turnaround at the Britannia Stadium as Mark Hughes claimed his first win as Potters boss.
Marouane Chamakh capitalised on some poor defending from Ryan Shawcross and Robert Huth to give the visitors the lead with a neat finish just past the half-hour mark.
The Potters should have been level almost immediately but Peter Crouch could only find the crossbar with his header before Julian Speroni almost deflected the ball into his own net.
However, Stoke finally found a breakthrough shy of the hour mark when Charlie Adam converted with a tidy finish at the back post, and the turnaround was completed four minutes later when Shawcross powered home from eight yards out to take all three points.
Southampton scored a late equaliser to deny Sunderland all three points at St Mary's as Paolo Di Canio's men failed to hold on in the final minutes and had to settle for a 1-1 draw.
Emanuele Giaccherini gave Sunderland the perfect start when heading in Sebastian Larsson's corner, before Jay Rodriguez was denied a quick-fire equaliser after being questionably flagged offside.
Record signing Pablo Daniel Osvaldo was introduced by Southampton at the start of the second half, but it was Jose Fonte who finally found the breakthrough with three minutes remaining when glancing his header past Keiren Westwood from James Ward-Prowse's free-kick.
Robbie Brady scored Hull's first goal on their return to the Premier League as Steve Bruce's side enjoyed a 1-0 win against Norwich despite going down to ten men.
Brady converted from the penalty spot midway through the first half to give the home side the lead after Michael Turner was judged to have brought down Sone Aluko inside the box.
Minutes after going in front, Hull saw Yannick Sagbo dismissed for tangling with Turner, but Norwich could not make the extra man count.
Roberto Martinez's first home game in charge of Everton ended in a 0-0 draw against West Brom.
The Toffees enjoyed the lion’s share of possession and played attractive football, but could not find the finishing touch.
Marouane Fellaini and Seamus Coleman both saw efforts come back off the woodwork in the dying minutes of the game, as the sides had to settle for a share of the spoils at Goodison Park.
Newcastle could not find a way past West Ham as their match at St James' Park ended in a goalless draw.
Kevin Nolan wasted a glorious chance to score against his former employers when heading wide from six yards out, while Shola Ameobi's cross-cum-shot looped over a hapless Jussi Jaaskelainen and back off the post in second half injury time.