Robert Snodgrass scored a late equaliser as Norwich held 10-man Tottenham to a 1-1 draw at White Hart Lane.
Tottenham were on course for their first win of the season as impressive debutant Mousa Dembele gave Spurs a second-half lead, only for Snodgrass to pounce to continue Tottenham's indifferent form under manager Andre Villas-Boas.
Andy Carroll inspired West Ham to a comfortable 3-0 win over Fulham at Upton Park.
West Ham's new signing dominated Fulham's backline before limping off with injury as first-half efforts from captain Kevin Nolan, Winston Reid and Matt Taylor secured all three points.
Everton and Swansea failed to maintain their impressive starts to the season as both sides lost their 100% records.
David Moyes' Everton went down 2-0 to West Brom at the Hawthorns while Swansea battled to a 2-2 draw with Sunderland at the Liberty Stadium.
Meanwhile, a Peter Crouch strike 14 minutes from time snatched a draw for Stoke against Wigan at the DW Stadium.