Spurs were joined on nine points by Chelsea who also won their third successive league match with a 2-0 victory at near-neighbours Fulham.
While promoted Burnley followed up their shock 1-0 win over champions Manchester United on Wednesday with another 1-0 victory over Everton, who finished fifth last season.
David Moyes' team, who he admits have been unsettled by the Joleon Lescott transfer saga, prop up the table after losing both their opening matches.
Spurs have made their best start to a season since 1960-61 when they won their first 11 league matches and went on to win the FA Cup and League double.
Their success at Upton Park came courtesy of two mistakes by West Ham who gifted goals to ex-Hammer Jermain Defoe and Aaron Lennon after Carlton Cole had given West Ham the lead in an exciting, open London derby.
Spurs manager Harry Redknapp refused to compare the current side to the 1961 team, but told reporters: "I was delighted with the performance, we showed a lot of character after going behind.
"We've got the smallest forward line in the world with Jermain Defoe, Robbie Keane and Luka Modric but we'll go for it."
The Hammers went ahead just after the break when Cole, in front of watching England manager Fabio Capello, scored a blistering goal with a shot on the turn which Spurs keeper Carlo Cudicini had no chance of saving.
However, Cole turned from hero to villain within five minutes when he inexplicably passed back from midfield straight to Tottenham striker and England colleague Defoe, who lashed the ball past goalkeeper Robert Green from the edge of the box for the equaliser and his fourth league goal of the season.
Spurs went ahead with around 10 minutes to go when Lennon took advantage of a slip by West Ham defender Jonathan Spector to curl home the winner from the edge of the box. That goal gave them the points and a goal difference of plus-6 compared to Chelsea's plus-5.
SHORT TRIP
Chelsea, tipped to launch a strong challenge for the title under new coach Carlo Ancelotti, made the short trip back to Stamford Bridge with all three points after goals from Didier Drogba and Nicolas Anelka secured victory at Fulham.
Drogba put Chelsea ahead after 39 minutes when he was played through by Anelka and slotted the ball past Mark Schwarzer with Anelka making sure of the points by scoring after a quick Chelsea breakaway 14 minutes from time.
Burnley overcame Everton courtesy of a 34th minute Wade Elliott goal.
Burnley, who saw United's Michael Carrick miss a penalty in their shock midweek win over the champions, enjoyed similar fortune when Everton's French striker Louis Saha fired wide with his second-half spot kick.
That left Burnley, back in the top division for the first time for 33 years, in seventh place with six points from their opening three games.
Burnley manager Owen Coyle told the BBC: "We knew we were going to have to be at our best today and in the opening period somne of our football was terrific. Everton had a lot of the ball in the second half and we had to be brav
