Brown had only just come on when he bundled the ball in from point blank range in the 73rd minute but the offside flag denied him.
The visitors were marginally the better team early on with James Stevenson missing a half chance and Ross Hamilton surviving a heavy challenge and going for goal when others would have dived in search of a penalty.
Michael Bolochoweckyj then produced a real defender's finish as he blazed over the top from 12 yards.
Alloa keeper James Evans was finally called into action after 29 minutes when he was tested by Steven Bell, and shortly before half time, Paddy Connolly failed to make contact with a searching cross from former Rochdale midfielder Shaun McClair who was playing as a trialist.
Striker Robert Dunn went close early in the second period with an angled drive and Bell panicked when unmarked at a corner kick but Alloa created the clearer opportunities.
Home goalkeeper Rob Giacomi made three excellent saves from John Ovenstone, Bolochoweckyj and Andy Brown and even when the other Brown eventually got the better of him, the offside flag came to Stirling's rescue.