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 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."
A good win from a game we dominated. Could have done our goal difference a great deal of good tonight. We should have scored at least another 3 or 4 goals. Won't get away with being that wasteful against th arsenal.- rapscallions