Striker Wayne Andrews grabbed the vital goal eight minutes after half-time when he ran on to a long ball from strike-partner Stephen Brooker before out-muscling Blackpool's midweek goal hero Michael Jackson and slotting past Rhys Evans.
It was no more than Gary Johnson's outfit deserved. They came out stronger and created most of the early chances with the partnership of Brooker and the on-loan Andrews as well as set pieces from manager's son Lee Johnson creating many of the problems.
But there were also challenges for Johnson senior as he was forced to make three injury changes within the first hour.
For Blackpool, beaten after extra-time in midweek, Keigan Parker went closest in the first half with a shot from the edge of the area which almost beat Adriano Basso despite coming of the Scot's weaker left foot.
Andrews' goal clearly changed the dynamics of the game and Bristol's 3-5-2 system became more of a 5-3-2, but the second half still saw chances at both ends.
Andrews almost doubled his tally on the hour-mark with a neat shot on the turn which had relatively little power but it hit the post and bounced out.
A couple of minutes later Shaun Barker went close with a scorching shot from distance which looked for a moment to be going in but ended up a yard wide.
Brooker, finding a little more space as the home side pressed forward, also had a chance to double Bristol's advantage 11 minutes from time with a low drive from outside the area which went just wide.
Blackpool continued to press until the end with substitute Ben Burgess going close with a header and Keith Southern seeing a helpful long-range lob go just over the bar.