Leading scorer Jamie Cureton scored his 13th of the season, a goal which proved enough to give the Grecians their first win at Valley Parade for 29 years.
The 37-year-old striker, who played in the same Reading team as Bradford manager Phil Parkinson, rounded off a superbly worked goal two minutes before half-time, hooking the ball home after Craig Woodman's cross to the far post had been headed back into the goalmouth by Matt Oakley.
Tisdale, delighted with the resilience shown by his team as Bradford pressed hard for a second-half equaliser, said: "It was a super goal and well worked with a fine assist from Matt Oakley. The goal gave us something to defend in the second half and we managed to see it through.
"I thought we stuck at it well and restricted Bradford to one or two half chances. It is another three points and this away win is as good as it can be at a place like Bradford because I am sure they are going to promotion candidates. It was a good 1-0 win.
"We matched Bradford in the first half, played our football and created some good chances before scoring a super goal."