After a quiet opening to the game, the home side were first to threaten when, with 10 minutes on the clock, Paul McManus advanced on goal from the right-hand side of the pitch, firing in a low angular shot which rebounded from the legs of City keeper Craig Nelson.
The visitors responded a minute later with a clever move involving strikers Paddy Connolly and Chris Geddes, the latter then teeing up Steven Hampshire, whose shot was blocked by the well-positioned Mark Campbell.
David White came close for Brechin and Steven Manson almost scored for Raith as either side traded pounches in the search for the opener, which arrived in rather bizarre fashion in the 17th minute.
Brechin's Hampshire sent in a harmless-looking cross from the right and Raith's Brian Fairbairn attempted to cushion the ball on his thigh in order to steer it into the arms of goalkeeper Michael Brown. The midfielder misjudged his touch however, and the ball sailed past the helpless Brown and into the net.
Veteran striker Paddy Connolly then tested Brown with a low shot from the edge of the box as Michal O'Neill's men finished the first half strongly.
Raith began the second half in positive manner, and Manson should have equalised five minutes after the break, the Rovers midfielder firing over the bar from close range following a deep cross from Bonar on the right.
The scores were levelled, however, in the 72nd minute when McManus was brought down in the box by David White with Ian Harty slotting home the resultant penalty kick.
Brechin did have a chance to restore their advantage late in the game when Iain Russell found himself in the clear, but the City substitute shot tamely into Brown's arms.