Robin van Persie scored his first goal for Manchester United to help them to a 3-2 win over Fulham, while Chelsea made it three wins from three against Newcastle.
Tottenham were denied their first win of the campaign after being held to a 1-1 draw by West Brom at White Hart Lane thanks to James Morrison's late strike
Swansea maintained their perfect start to the season with an impressive 3-0 success over West Ham, while Everton also made it two from two against Aston Villa.
Wigan spoiled Southampton's first home game back in the Premier League with a 2-0 win at St Mary's.
Norwich and Queens Park Rangers bounced back from their heavy defeats last weekend to share the spoils after a 1-1 draw at Carrow Road.
Manchester United bounced back from Monday's defeat by Everton with a narrow 3-2 win over Fulham at Old Trafford.
Fulham stunned the home side when they broke the deadlock after just three minutes through Damien Duff after a well-worked free-kick routine.
Bryan Ruiz rolled a free-kick from the left-hand side of the box towards the penalty spot to Duff who placed his shot into the bottom corner of the net past David de Gea.
The goal stung United into action and they drew level seven minutes later with Van Persie announcing himself to the Old Trafford faithful with a stunning effort.
Patrice Evra swung over a cross from the left and Van Persie with his back to goal got in ahead of Brede Hangeland to hook a superb first-time effort past a stranded Mark Schwarzer.
United hit the front on 35 minutes with fellow new boy Shinji Kagawa getting off the mark with a close-range finish.
Tom Cleverley fired in a shot from the edge of the box which Schwarzer failed to hold and Kagawa was on hand to prod the ball home.
The home side added a third four minutes before the break as Rafael Da Silva netted his first goal in three years as he headed home Ashley Young's inviting cross at the far post.
Fulham were handed a route back into the game on 64 minutes with an unfortunate own goal from Nemanja Vidic.
De Gea made a mess of coming for a cross from the left and Vidic inadvertently deflected the ball into his own net with his heel.
Worryingly for United, Wayne Rooney, who was dropped to the bench, had to be stretchered off late on after cutting open his leg in trying to block a shot from Hugo Rodallega.
Eden Hazard was Chelsea's main man once again as he produced another impressive performance for the Blues, teaming up with Fernando Torres to inspire a 2-0 victory over Newcastle at Stamford Bridge.
The Belgium international converted an early spot-kick for the Londoners after Torres had been caught in the penalty box by Vurnon Anita, making his full Newcastle debut.
Hazard then laid on the second goal for Torres in first-half stoppage time and the frontman made no mistake toe-poking it home.
Newcastle fought back in the second half, with a notable chance coming when Papiss Cisse missed a header from close-range, but they could not find a response as the Blues went top of the fledgling table with three wins from three.
Swansea continued their excellent start to the Premier League season with a convincing 3-0 win over West Ham at the Liberty Stadium.
Goals from Angel Rangel, Michu and Danny Graham were enough to give Michael Laudrup's side their second win in two games and condemn West Ham to their first defeat.
Andre Villas-Boas is still looking for his first win in charge of Tottenham after West Brom left it late to earn a 1-1 draw.
After a goalless first half Spurs finally made the breakthrough 16 minutes from time with a rare effort from Benoit Assou-Ekotto.
The ball dropped to Assou-Ekotto on the edge of the box and his shot through a packed penalty area took a slight deflection before finding the bottom corner of the net past a stranded West Brom keeper Ben Foster.
West Brom refused to give up and grabbed a point with Morrison's late leveller when he capitalised on some slack defending from the home side.
Sunderland's clash with Reading was called off after torrential rain on Wearside.
Referee Neil Swarbrick postponed the fixture at around 1.40pm after several inspections, with managers Martin O'Neill and Brian McDermott both having viewed the playing surface for themselves.
Everton maintained their perfect start to the campaign with a 3-1 win over Aston Villa at Villa Park to inflict a second successive defeat on Paul Lambert's side
Everton got off to a flying start when Steven Pienaar fired them in front after just three minutes with a superb shot from the edge of the box after being teed up by Steven Naismith.
Things got worse for the home side just past the half-hour mark when Phil Jagielka powered down the right and crossed for Marouane Fellaini whose header somehow squirmed through the arms of Shay Given.
Everton made it 3-0 two minutes before the break as Nikica Jelavic scored his first goal of the season with a superb finish from Leighton Baines' pull-back.
Villa were reduced to ten men just before the hour mark when Ciaran Clark was sent off for a professional foul after bringing down Jelavic as he tried to race clear on goal.
Villa pulled a goal back 16 minutes from time as Karim El Ahmadi scored his first goal for the club with a long-range strike that somehow evaded Tim Howard in the Everton goal.
Norwich and QPR picked up their first points of the season after a draw at Carrow Road.
Norwich broke the deadlock after 11 minutes when Simeon Jackson headed home Anthony Pilkington's cross from close range after a fine flowing move from the home side.
QPR were gifted a route back into the game eight minutes later when they were awarded a soft penalty after referee Mark Clattenburg adjudged Canaries debutant Sebastien Bassong to have fouled Djibril Cisse inside the box.
Cisse took responsibility from the spot and his effort was saved onto the post by John Ruddy, but unfortunately for the Norwich keeper Bobby Zamora reacted quickest to fire the ball into the unguarded net.
Southampton slumped to their second straight defeat after going down 2-0 to Wigan.
After a goalless first half Wigan broke the deadlock six minutes into the second half when Shaun Maloney played in Franco Di Santo and he fired his effort high into the net past Kelvin Davis.
Wigan put the game beyond Southampton when Arouna Kone robbed Jose Fonte of the ball to run through and fire past Davis.