The ITV cameras came to the Conference South side's stadium in the hope that they could cause an upset against the Football League's bottom club but Aidy Boothroyd's men were professional from the word go, forcing the issue from the start of the game and creating a number of chances before Danny Emerton and Jacob Blyth scored the vital goals.
Town, for whom Chris Hackett was a constant thorn in Bishop's Stortford's side, then withstood a late goal from the hosts to take their place in Round 2 of the competition where a trip to either Grimsby Town or Scunthorpe awaits.
"It was a really tough game," said Boothroyd afterwards.
"They're a very lively team and we stood up to the task. I thought we were excellent. We created lots of chances. It's indicative of our season, creating chances but not having the knack of putting them in the net.
"We made it difficult for ourselves after we scored. Credit to our opposition, they made it a tough game.
"They get a goal at the end and it gives them renewed energy and vigour. In the end we managed to see it out. The only disappointment for me, if there is anything, is that we didn't score more goals."