The Hammers scored three stunning goals in 13 second-half minutes to come away with their first victory at White Hart Lane since 1999.
Winston Reid started the rout with a goal from a corner, Ricardo Vaz Te made doubled the lead and then Ravel Morrison scored a superb solo strike to seal a memorable triumph.
Sam Allardyce had described his West Ham team as "relegation favourites" earlier this week, but on this evidence, the east London side will have no trouble staying up.
Much had been made of West Ham's lack of goals this term because of the absence of Andy Carroll, but the way in which the Hammers took their goals will delight Allardyce, and the visiting fans, who revelled in gaining the bragging rights over one of their arch rivals.
As for Tottenham, the bubble of happiness that came with the arrival of seven new players has now burst. Boos rang out from the home fans at the final whistle. They know there is still much work to do if they are to mount a top-four challenge.
The Baggies, fresh from downing Manchester United last weekend, had ample opportunity to extend their lead after Claudio Yacob headed home a Morgan Amalfitano cross in the 42nd minute.
But it was Arsenal who ended the game in the hunt for the points after Wilshere, looking to replace reports of late night smoking with more positive headlines, scored with a deflected first-time shot from 20 yards.
The result was enough to see them edge ahead of Liverpool but only on goals scored while West Brom are up to 12th.
Jose Mourinho's men made the 120-mile journey to Carrow Road by plane on Saturday and made a flying start when Oscar gave them a fourth-minute lead after Demba Ba's lay-off from Frank Lampard's lofted pass.
Victory from then seemed a formality for Chelsea but it appeared anything but until a late rally.
Ba might have netted early in the second half following a cross from Ramires, who was relieved not to concede a penalty when challenging Anthony Pilkington in the box.
Norwich levelled when Pilkington headed in from close range and had further opportunities, but Hazard finished off a ruthless counter attack and Willian curled in his first Chelsea goal to complete the win and they ended the day in third - two points behind Arsenal and Liverpool.
Adam Lallana opened the scoring in the 19th minute and substitute Jay Rodriguez added the second seven minutes from time.