The Welsh winger struck twice, while Gylfi Sigurdsson also scored for Andre Villas-Boas' side who came back from 2-1 down to take the three points.
Bale put Spurs ahead before an Andy Carroll penalty and a Joe Cole strike put the home side ahead, but Spurs ran out victors with Bale's superb 90th.minute strike - his 15th Premier League goal of the season - securing a win which sees them jump above Chelsea and into third.
"It was a massive victory," he said on Sky Sports 1.
"We knew after the (Chelsea) result yesterday [Sunday] that we had a massive chance to get third spot. We deserved the victory.
"We know what we are capable of. We have scored a lot of last minute winners.
"We are confident that if we keep battling to the end we will score.
"I'm just enjoying my football. The most important thing is the team playing well. It is not about me it's about the team."
Villas-Boas was full of praise for Bale after the game.
"He is an unbelievable, super talent. You have seen him this season go to another level and make a difference every game. Tremendous talent for sure."
Spurs are now five points behind Manchester City in second and seven clear of fifth-placed Arsenal, who they take on this weekend.
"We just have to keep getting points," Villas-Boas added. "We want to get the most we can get.
"Obviously the distance isn't big to second.
"We face Arsenal Sunday and it is a big opportunity to build the distance to them and that is first on our minds.
"Our priority is to establish our position and hopefully get more comfortable distance to Chelsea and Arsenal.
"It's going to be a game full of passion. To put Arsenal seven points away is a better margin, but it is not finished, seven points is not enough."
West ham boss Sam Allardyce bemoaned Matt Taylor's miss when the score was at 2-1, but like Villas-Boas hailed Bale's winner.
"It is one of the 'worldies' he continues to produce," he said. "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."
Allardyce was disappointed with referee Howard Webb, believing Spurs midfielder Mousa Dembele should have seen red.
Kevin Nolan had to be replaced following a tackle by the Spurs midfielder, who Allardyce believes should have been booked for a second time after fouling Cole.
"You look at consistent bookings that Howard gave to our players after. Dembele after that fouled Mo Diame just inside after he nicked the ball off him and he let that one go.
"Where he got that wrong in the second half there is a ball over the top and he pulls Joe Cole back then he kicks the ball away.
"You do that, Howard you have to send him off, that's what we are told.
"I'm really disappointed by that."