Tottenham Hotspur built on their first game win over Liverpool by hammering Hull City away from home and Birmingham City snatched a last-gasp win at home to Portsmouth.
Burnley marked their first home match in the top flight for 33 years with a memorable 1-0 win over Manchester United courtesy of Robbie Blake's stunning volley.
Blake smashed an unstoppable shot inside Ben Foster's near post after 19 minutes to earn the promoted Clarets a deserved win at Turf Moor.
Owen Coyle's side were indebted to Brian Jensen for claiming a famous victory, with the Burnley keeper saving Michael Carrick's 44th minute penalty after Blake had brought down Patrice Evra.
Liverpool ignored pre-game speculation over Rafa Benitez's future to record a comfortable 4-0 triumph over Stoke at Anfield.
Fernando Torres broke the deadlock after just four minutes to set Liverpool on their way and new signing Glen Johnson doubled the lead on the stroke of half-time.
The hosts created numerous chances to increase their advantage and finally notched a third goal on 78 minutes when Dirk Kuyt scored from close range after excellent work by Steven Gerrard before David Ngog headed in a late fourth.
Jermain Defoe scored a clinical hat-trick as Spurs thumped Hull 5-1 at the KC Stadium to make it back-to-back wins at the start of the season.
Spurs were 3-1 up at half-time with Defoe having scored twice and Wilson Palacios also on target for the visitors, while Stephen Hunt replied for the Tigers.
Robbie Keane, who had been involved in two of the earlier goals, headed home the fourth on 78 minutes before Defoe completed his treble in the final minute with a blistering drive from the edge of the box.
Birmingham left it late to secure a first win back in the Premier League after James McFadden's last minute penalty clinched a 1-0 success at home to Portsmouth.
Scotland international McFadden kept his cool from 12 yards to fire past Pompey keeper David James, who was penalised for bundling over Sebastian Larsson.