Brechin opened the scoring in the seventh minute when Paddy Connolly played in Darren Smith and he shot under goalkeeper Scott Black.
In the 19th minute Kevin Byers burst forward and shot just wide of the post while at the other end five minutes later Michael Moore headed wide from Mark Crilly's free-kick.
In the 28th minute Byers drove over after Stuart Callaghan had laid a free-kick into his path but the game boiled over a minute before half-time when Moore was sent off for elbowing Stuart Callaghan.
Moore then earned himself a second red card for returning and striking Callaghan as he lay on the ground.
Brechin looked for more goals and, in the 52nd minute, Scott Walker headed just over from Byers' corner.
Brechin made it 2-0 in the 60th minute when John Ward was pushed as he went for a high ball and Iain Russell scored from the spot.
Just two minutes later Darren Smith crossed to the back post and Russell scored with a beautiful volley.
Stranraer kept fighting right to the end and might have got a goal back in the 73rd minute when Stevie Nicholas forced a fine save from home keeper Craig Nelson.
Midfielder Nicholas again went close to grabbing a consolation goal for the visitors when he forced another good save from Nelson five minutes later.