Spurs had the chance to close to within a point of third-placed Chelsea, who lost at Newcastle yesterday, but the Baggies gave precious little away in the first half.
The dismissal of Goran Popov in the 47th minute changed the game in Tottenham's favour, though, and Bale duly secured all three points with a spectacular solo goal.
The win saw Andre-Villas Boas' pull three points clear in fourth after Everton were held by Aston Villa on Saturday, and Bale told Sky Sports 1: "It's massive. We spoke before the game because other results went our way yesterday [Saturday] and that gave us a big chance to capitalise. Thankfully we did.
"I think all the lads worked very hard and they deserved the victory."
Bale, who is thriving in a new central role alongside Clint Dempsey, found himself within shooting range in the 67th minute, his left-footed drive beating Ben Foster from just outside the box.
"I enjoy it," he added. "It's a role that I'm learning season by season. I've come inside more often than previous seasons and it's a role I'm enjoying.
"It's a new experience for me, a chance to improve my game and it gives me another dimension."
Germany international Lewis Holtby made his second Spurs appearance from the bench and revealed he is settling in well at White Hart Lane.
He said: "The lads are all making it easy for me to play. It's a fantastic club and I enjoy coming in every day.
"It's a massive boost to get the three points away (from home). It's unbelievable.
"If we have games like today [Sunday] and get the three points then it's a massive relief. I'm just happy to be at the club."
Villas-Boas admitted he would consider using Bale as an out-and-out striker after Jermain Defoe suffered a first-half ankle injury that is likely to sideline him for a number of weeks - in addition to forcing his withdrawal from the England squad to face Brazil at Wembley on Wednesday.
"We started today with Bale through the middle and Clint Dempsey on the left," said Villas-Boas. "It is something he feels comfortable with.
"It gives us even that possibility for sure. It is something we have to look to."
On Defoe's injury, Villas-Boas said: "He will have a scan and only when we see the results will we know the extent.
"It is a big blow because he is an important player and person for us, on and off the pitch."
Tottenham have collected four points from two away games at Norwich and Albion in the space of four days, and Villas-Boas admitted: "It has been a very important week for us.
"To get four points away from home, with not much time between the games, is excellent.
"We have put ourselves in a very good position to threaten for third place.
"I am extremely happy apart from the big setback to Jermain Defoe."