Spanish striker Michu hit his fourth goal in three league games but Swansea City missed the chance to top the fledgling Premier League standings after the Welsh side were held 2-2 at home by Sunderland on Saturday.
Everton also lost their perfect record after goals from Shane Long and Gareth McAuley secured a 2-0 victory for West Bromwich Albion at The Hawthorns.
Chelsea, who are not in league action this weekend after playing in the UEFA Super Cup, have a maximum nine points, followed by Swansea and West Brom on seven.
New Tottenham Hotspur signing Moussa Dembele came off the bench to score on his debut but coach Andre Villas-Boas was left waiting for his first win in charge after Robert Snodgrass scored five minutes from time to earn Norwich City a 1-1 draw at White Hart Lane.
Striker Andy Carroll enjoyed a bitter sweet debut for West Ham United after joining on loan from Liverpool, helping set up a first-minute goal in a 3-0 demolition of Fulham before suffering a second-half hamstring injury that could sideline him from England’s opening two 2014 World Cup qualifiers.
Champions Manchester City, with four points from their opening two games, host Queens Park Rangers at 1630.
Swansea’s impressive start to the season was checked by Sunderland and new signing Steven Fletcher at the Liberty Stadium.
Having scored eight times without reply in two games, Michael Laudrup’s side conceded for the first time when Sunderland cquisition Fletcher netted twice late in the first half, either side of a fine Wayne Routledge goal.
Michu continued his rich seam of form with a 66th minute equaliser but Swansea’s hopes of pressing for victory suffered a blow when Spanish central defender Jose Manuel Flores, known as Chico, was sent off 19 minutes from time.
Swansea confirmed later that left back Neil Taylor had suffered a fractured ankle during the first half.
West Brom, who beat Liverpool on the opening day, notched a notable city double by proving too strong for Everton.
Substitute Peter Odemwingie made an instant impact by picking out Long to score the opener on 65 minutes before McAuley made sure of the points with a late header.
Belgian playmaker Dembele lifted Tottenham’s spirits with a fine goal after moving across the capital from Fulham but fans filed out of White Hart Lane in despondent mood after Snodgrass secured a deserved point for Norwich.
Dembele rifled past John Ruddy on 68 minutes but substitute Tom Huddlestone was then sent off and the final whistle was greeted by a chorus of boos with Spurs picking up only two points from their first three games.
New Spurs signings Hugo Lloris and Clint Dempsey were not registered in time to play.
West Ham eased past Fulham after Kevin Nolan netted after 53 seconds at Upton Park. Winston Reid and Matt Taylor added further first-half goals but Carroll, who impressed on his debut, limped off midway through the second half.
Manager Sam Allardyce said the striker will “probably be on our treatment bench for a while”.
Wigan Athletic twice led at home to Stoke City but had to settle for a 2-2 draw.