After Harry Kane opened the scoring for Spurs in the 13th minute, Jose Mourinho's side conceded a controversial equaliser in the second-half as Tariq Lamptey finished calmly despite an apparent foul in the build-up.
In search of the win, Mourinho opted to bring on Bale in the 70th minute and the Real Madrid loanee repaid his manager's faith with a headed goal just three minutes later.
Bale's first Spurs goal since May 2013 proved decisive, and though he enjoyed the feeling of finding the back of the net, he was quick to stress the focus should remain on the team.
"It's a great feeling. You just want to come on and do a job for the team. I worked for the team and was lucky enough to get the goal," Bale told Sky Sports post-game.
"It was obviously great play from Sergio Reguilon and I was in the right place at the right time. It's nice to get off the mark.
"Everyone always talks about individuals but I've always said I’m a team player, I'd be happy coming on doing a job even if it's defending. The most important thing is the collective.
"We are growing every game. Even if we make mistakes we are learning from them and we can only use that as a positive. I haven’t played a lot of football. I had a little problem with my knee so it’s taking a bit of time. I am working hard in training and when I get chances."
Tottenham have jumped up to second with the win, only two points behind leaders Liverpool, and Bale believes Spurs can compete with the best if they remain focused.
"Very competitive, we know not to get too carried away. There are some great teams, we are just going to keep working as hard as we can," Bale added.
Kane was delighted to see Spurs seize the chance to go third and was stoked to see Bale get his name on the score sheet.
"We said it was a great chance to go second in the league and put ourselves up there. We had to grind it out," Kane said.
"I'm delighted for Gaz to come on and make an impact and that's what we need to win games. He's had a mini pre-season with us, it's about getting fit and sharp, we all know what he can do at the highest level. Every game he'll get stronger, we need every player to make an impact.
"We have let points slip and today could have been similar but we are learning - these games are the ones you need to grind out."