Manchester City grabbed two goals in the second half to end Hull City's resistance, while there were first wins of the season for Newcastle and Norwich, with Stoke making it back-to-back victories and Everton having to settle for their third draw in as many league games.
Manchester City bounced back from their surprise defeat last weekend by beating Hull City 2-0 at the Etihad Stadium thanks to goals from Alvaro Negredo and Yaya Toure.
Having wobbled in defence in falling 3-2 to Championship-winners Cardiff after taking the lead, City managed to avoid a loss to another promoted side. However, they were frustrated for over an hour and made the breakthrough via substitute Negredo after he headed in Pablo Zabaleta's cross in the 65th minute.
With Hull chasing the game towards the end, their hopes of snatching an equaliser were dashed as Toure curled in a free-kick to seal the three points.
Newcastle enjoyed their first league win of the season, with Hatem Ben Arfa firing them to three points at home to Fulham with the only goal of the game.
For the second league game in succession, Yoan Gouffran was guilty of an incredible late miss. Having blazed over the bar from five yards out against West Ham last week, Gouffran planted a free header from a similar distance wide of the post late in the second half. But Ben Arfa spared his team-mate's blushes by hammering the ball home from the edge of the box on 86 minutes.
Nathan Redmond's second-half strike proved to be enough as Norwich saw off Southampton 1-0 at Carrow Road. Redmond provided the first goal of the 3pm kick-offs, cutting inside from the left and drilling home with his right foot on 68 minutes, with Southampton failing to find a response.
Stoke recorded their second league win of the season, courtesy of a 1-0 victory against West Ham at Upton Park. The game was settled with eight minutes remaining by substitute Jermaine Pennant, who stepped up to curl a free-kick from 25 yards out over the wall and into Jussi Jaaskelainen's bottom corner.
Cardiff failed to make it back-to-back victories after they played out a 0-0 stalemate with Everton in Wales. Marouane Fellaini and Leighton Baines were both included in Roberto Martinez's starting line-up, despite the questions surrounding their Everton futures amid interest from Manchester United.
The Toffees were denied a penalty late in the first half when Baines burst into the box and appeared to be felled by Gary Medel, with neither side able to find a breakthrough.