The Hammers conceded to Gareth Bale in the 13th minute before Andy Carroll (25th minute) and Joe Cole edge them ahead prior to the hour-mark but Gylfi Sigurdsson and a Bale special saved the day for Spurs.
At 2-1, West Ham winger Matt Taylor could have given the home side a healthy advantage but he failed to produce the goods before Bale again came up with another stunning winner.
"It is one of the 'worldies' he continues to produce," he told Sky Sports. "You think at some stage he has run out of them but he has not. I think that is the best one.
"In the end, the way he has hit it, there is not an awful lot you can do about it.
"We made a terrific go of it. It was at a crucial stage when Matt Taylor got through one on one and their keeper made good save, we want to be scoring that.
"At 3-1 there is no way back for them. They've got the goal then they scored a 'worldie'.
"We have been beaten by Gareth Bale really. I thought the lads caused them a lot of problems."