And debutant Bryan Prunty slotted past goalkeeper Chris McCluskey to extend the Wasps' advantage 10 minutes later.
Stenny's Scott Dalziel and Sean Welsh had efforts saved and the home side's Christopher McLeod also volleyed over.
Stenhousemuir: McCluskey, Lyle, Smith, McLeod, Stephen Thomson, Iain Thomson (Molloy 46), Welsh, Currie, Motion, Bradley (Diack 46), Dalziel, Diack (Love 48). Subs Not Used: Bennett, Pat Scullion.
Alloa: Crawford, McClune, Walker, Townsley, Bloom, Brown Ferguson, Grant (Carroll 71), Brown (Kerr 90), Scott, Prunty (Gormley 67), Noble. Subs Not Used: Hall, Buist.
Goals: Brown Ferguson 15, Prunty 25.
Ref: G Salmond
Source: BBC Sport