With a strong wind and driving rain in their faces, the visitors defended for their lives and conceded only once to a deflected header from substitute Wes Burns eight minutes from time.
First-half goals from Franck Moussa and Andy Webster had put Coventry in command in atrocious conditions. It took a tremendous effort by groundstaff at half-time to clear surface water and ensure the game was completed.
A delighted Pressley said: "We played some great football in the first half and then showed tremendous character with our backs against the wall in the second half.
"Facing such a strong wind, we were penned in at times, but I made a couple of tactical adjustments to help us defensively and I couldn't be more proud of my players.
"They have come a long way in a short time and we are still developing as a side. This is a tremendous result for us because Bristol were coming off a good home win on Saturday.
"We suffered a setback at Leyton Orient in our last match but one thing this group of players have shown is that they can bounce back from poor results."