The tie was a rearranged game following the abandonment of the original fixture 10 days ago due to Fabrice Muamba's cardiac arrest.
Spurs were left frustrated by Wanderers keeper Adam Bogdan during the first period, as the Hungarian produced countless saves to keep the game goalless.
He was then called upon to save from Bale at the near post and once more to push away Scott Parker's effort from the edge of the box.
Even when the hosts did eventually beat Bogdan, they were denied by the woodwork when Rafael van der Vaart's free kick struck the bar.
Finally Spurs were able to gain a lead, with the goal coming from an unlikely source in the shape of Ryan Nelsen.
The centre half powerfully headed into the top corner on 74 minutes to end Bolton's resiliency, which was further dented by Spurs' second moments later.
After being denied by Bogdan on multiple occasions earlier in the game, Bale eventually beat the Bolton stopper when he shot in following Jermain Defoe's pass.