Bale's low drive gave Tottenham the lead, but West Ham produced a determined response as Andy Carroll levelled with a penalty before Joe Cole made it 2-1 in the second half.
Spurs launched a rally and Gylfi Sigurdsson poked home a leveller before Bale's 90th minute thunderbolt into the top corner sent his side into third place in the Premier League.
Reflecting on the Welshman's display, Villas-Boas told Sky Sports: "Such a special talent and I think we've been able to see him this season in another level. He's just making the difference in every single game.
"I think the team did very, very well. Jaaskelainen to be the man of the match in a game which finishes 3-2 also explains why we had to leave it late with Gareth to win this game."
When asked whether Bale is world class, the Portuguese said: "Well I think for some time already.
"Players like this are able to assume the responsibility in these moments and I think from the clips you're seeing, receiving the ball in midfield, taking it forward, being fouled, getting up and then just lining up the shot to score the winning goal. Tremendous, for sure."
Spurs are now five points behind Manchester City in second, but Villas-Boas insists he is focusing on extending the current four-point gap over 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 on 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."