Arbroath remain top of the Second Division following a fifth-straight league victory.
Scott Buist shot Brechin in front on 29 minutes before substitute Lee Sibanda's header from Mark Baxter's cross levelled the scores.
Steven Doris struck a confident penalty kick after Sibanda had been updended but Brechin hit back with a penalty of their own, netted by Paul McManus.
But a sweet curling effort from Gavin Swankie sealed the points.
Nelson, McLean, Smith, Buist, Dunlop, David Crawford, Fusco, Janczyk, McKenna (Hodge 80), Lister, Weir (McManus 80). Subs Not Used: Scott, Brady, King.
Buist 29, McManus 82 pen.
Hill,Baxter,McAnespie (Brown 89),Malcolm,Busch, Falkingham,Kerr,Gibson (Ardallany 70),Sheerin (Sibanda 32), Doris,Swankie. Subs Not Used: White,Girvan.
Sibanda 36, Doris 78 pen, Swankie 88.