Stirling turned in a much-improved display after crashing 3-0 at Alloa last week but still suffered their 10th defeat in the last 11 meetings with City, and must be glad the Angus side will be playing in a different league after the summer.
Brechin took the lead after just two minutes when Scott Walker was unmarked to head past Albion debut keeper Scott Christie, but Stirling reacted well to going behind. Robert Dunn thundered a superb shot against the bar, then Chris Aitken found the net with a crisp 20-yard volley only for the goal to be ruled out because Dunn was judged to be interfering with play.
The equaliser arrived on the half-hour when Stewart Devine picked out Paul di Giacomo, who teed up Dunn to sweep the ball home.
Charlie King then missed a great chance to restore Brechin's lead, only to grab what turned out to be the winner with a stunning strike four minutes before half-time. The former Stirling winger accepted a throw-in from James Sharp and lashed a fabulous 25-yard shot into the top corner.
The second half provided fewer thrills, but Albion were twice denied at the death when Paul Nugent sent a header on to the top of the bar and then the same player had a similar effort hacked off the line.