Darryl Duffy's penalty was enough to secure Cheltenham's passage into the second round of the FA Cup at the expense of League One Tranmere.
The League Two side were awarded the penalty after Lucas Akins tripped Sido Jombatti in the area, with Duffy firing into the top left corner.
Ash Taylor came close to equalising for Tranmere but his header shaved the outside of the post.
The home side continued to push forward but Cheltenham held out for the win.
VIEWS FROM THE DRESSING ROOM
Tranmere manager Les Parry told BBC Radio Merseyside:
"We just didn't get started and in the first half we didn't get into our stride.
"You suddenly think after half time you can throw a switch and lift your performance and it just doesn't work like that.
"You can't have two defeats and not think about changing the team and if the reserves perform on Tuesday, it will give me something to think about."
Cheltenham Town boss Mark Yates told BBC Radio Gloucestershire:
"I thought we were in control of the game, particularly once we scored, we had to defend - they threw everything at us and at the end they had five or six men in the box and were slinging things in.
"Scott Brown has had one shot to save and that's testament to our resolute defence, a decent keeper and the hard work that's gone on in front of them.
"We'll be back in next week working hard to make sure that we don't get bored of winning."