The Honest Men had the better of the first half and deservedly took the lead through midfielder Paul Weaver in the 35th minute. A Chris Strain cross from the left was missed by the Brechin defence and came straight to Weaver who made no mistake from around 18 yards.
Brechin tried hard to get back on level terms after the break and Paddy Connolly had a great chance to equalise in the 54th minute, but he blasted the ball over the bar from a good position.
However, the Honest Men hit back and wrapped up all three points in the 69th minute when Jerome Vareille picked up a David Dunn pass, swivelled neatly and then slotted the ball beyond the reach of City keeper Craig Nelson.
City tried to salvage something from the game in the final few minutes, but the Ayr defence were in an uncompromising mood and were giving nothing away.