The Bath side started the game well and took an early lead when Xander Davis crashed over from close quarters following a sustained period of early pressure. Johnny Batchelor then added a penalty to stretch the early lead.
Avon had the edge in the tight with Dan Cousineau, Davis and Josh Hiscott all making inroads into the Minehead defence. It was against the run of play when Minehead broke through to score under the posts.
The visitors kept to their game plan, mixing up the point of attack and, with the backs starting to find gaps, flanker Dan Griffin extended their lead with a well taken try, Batchelor added the extras to give Avon a 15 - 7 half time lead.
Avon got off to the worst possible start as they conceded a soft try within two minutes of the restart to bring the hosts back within a single point. This game was always going to be tight and shortly after Batchelor had slotted another penalty.
Once again Minehead got their third converted try to take the lead, only for the visitors to square it up again at 21 each as the full back was on target again.
Avon still had the majority of possession but the Minehead defence was resolute and, with a large home crowd cheering on every tackle, they were becoming hard to break down. With 10 minutes to go, fly half Tom Boreham spotted a gap and sliced though a scrambling defence to score under the posts, again converted by Batchelor.
Avon had not won at Minehead for several years and now sought to hold on to their 7 point lead. But it was not to be as they were undone by a speculative kick ahead and the unkind bounce of the ball as the Minehead winger got his hand to the touchdown first. An excellent conversion from the touch line pulled it level.
Avon did have a final chance to win the match but the 40m penalty attempt agonisingly drifted wide and they had to settle for the draw. The two points ensured that they retained 4th place in the Somerset Tribute Counties 2 league table.
On Saturday, Avon host unbeaten leaders Old Reds 2nds at Hicks Field.