This result pushed Wells up to 2nd place in Western Counties North whilst Avon remain rooted just above the danger zone.
Playing with the wind in the first half, Avon's powerful pack had the edge and their efforts were rewarded with a 6 points to 3 lead at half time, courtesy of two penalties from Rob Fitch.
After the break, the Wells backs started to play an increasingly influential role and scored 3 tries to turn the game on its head, two of which were converted plus two penalties to put the result beyond doubt.
Next Saturday, Avon travel to Old Bristolians.