The visitors played almost the entire game with 10 men after goalkeeper Aaron Howe was red-carded in the fourth minute for his foul on Luke Hubbins.
This led to the only goal of the game as Darren Byfield slotted home the penalty, beating replacement shot-stopper Sam Beasant, who had come on for Gavin McCallum.
The Bucks went close to a second goal in the 29th minute when Phil Trainer shot just wide.
The balance of the game saw the Cards having more possession despite their numerical disadvantage, but they could not make it count as the hosts kept their chances to a minimum.
But there was a late chance for Garry Hill’s side when Telford keeper Ryan Young did superbly to deny striker Bradley Bubb with an excellent save.