The right-back struck in the 20th minute, latching onto Finn Azaz's superb pass before finishing off the inside of the post.
Southampton appeared comfortable until Cameron Bragg received a second yellow card shortly before half-time.
Despite playing the remainder with 10 men, Saints held firm to claim a memorable south coast derby victory, leaving Bree delighted with his decisive contribution.
“It’s an unbelievable feeling, I’ve just watched the goal back,” he told club website.
“But the way that we did it as well, obviously being unfortunate to be a man down, and holding on for a clean sheet made it even more special.
“For me personally, for my goal to be the winner, and for the team, because we spoke about it over the break – adding clean sheets to our game and being more solid at the back.
“There’s no better way to do that, especially down to 10 men the boys dug in unbelievably. It’s just a massive win for the club.”