The goal was just reward for the visitors who dominated from the start with Breen commanding at the back and the midfield combination of Seyi George Olofinjana and Karl Henry too strong for the home side.
Over half an hour passed before the Wolves goal was threatened with Alan Mahon's right-foot shot from 25 yards flashing just wide of the target.
This was followed by amazing run down the right from Wade Elliott with the shot on the turn from Chris McCann that just missed the target.
Johnson was again in the thick of the action heading wide from 15 yards after good approach play by Rob Edwards and the cross from Daniel Jones.
The second half started in similar fashion with Wolves holding a firm grip on the game which caused Burnley boss Steve Cotterill into a double substitution after 52 minutes.
Burnley created an immediate opportunity with central defender Michael Duff heading wide from Mahon's corner.
Substitute James O'Connor fired over from the edge of the box and Mahon went close with a drive across the face of goal as Burnley pressed hard for the equaliser.
The home side's best opportunity for that equaliser fell to 18-year-old midfield player Chris McCann but he somehow put the ball over the cross bar from six yards.
At the over end Daniel Jones was unlucky not to put Wolves two in front when his left-footed free-kick struck the inside of a post with keeper Brian Jensen well beaten.
In stoppage time Jones again showed his ability at the dead ball with a free-kick which Jensen did well to tip over.
The result was a first defeat of the season for Burnley, who could have gone top had other results gone their way, but at the end of the day boss Cotterill was left to reflect that his side did not do enough to merit a victory.