The Glebe Park men, still looking for their first win of the campaign, held their own for much of the game but were left empty-handed when Willie Dyer deflected the ball into his own net.
Graeme Smith, the City keeper, was in action early on to deal with a rising Ally Roy shot while Mark Stewart did net for Sons only to be penalised for a foul.
At the other end Kalvin Orsi’s low shot forced the diving Scott Gallacher to turn the ball behind and from the resulting corner Sean Crighton headed over.
Dumbarton were desperately unlucky when Stuart Carswell’s netbound effort was deflected inches over.
Gallacher dived to pluck Liam Watt’s high shot out of the air as Brechin looked for that elusive win.
However, they were dealt the ultimate blow when the unfortunate Dyer deflected a cross from Chris McLaughlin wide of the helpless Smith.