Bale, who has scored eight times in his last six games, also netted the game's opener after 13 minutes but he left his best until the 90th minute when he unleashed a rocket of a shot past goalkeeper Jussi Jaaskelainen.
Spurs went two points clear of Chelsea on 51 points while West Ham dropped to 14th on a poignant night for the East London club, who honoured former player and England's 1966 World Cup-winning captain Bobby Moore on the 20th anniversary of his death.
A 25th-minute penalty from Andy Carroll and a Joe Cole strike in the second half brought the home fans more cheer until Iceland midfielder Gylfi Sigurdsson levelled for Spurs with 14 minutes remaining and Bale completed the visitors' comeback.
Former Finland keeper Jaaskelainen had been in brilliant form to deny Tottenham on several occasions but could do nothing but watch in desperation as Bale let rip from around 30 metres to break the hosts' hearts.
"He's a super talent. He's making the difference every single game," Tottenham manager Andre Villas-Boas told Sky Sports.
"We haven't been thinking like that," Bale said when asked if the team had thought it was not their day.
"We know what we're capable of and we're confident. We keep battling to the end. The team played really well."
