Grant Anderson levelled matters in the 57th minute when he neatly converted Stephen Murray's pin-point cross.
And Eric Paton completed the comeback with a fierce effort from the edge of the penalty area 12 minutes into the second half.
Alloa: Ewings, McClune, Gibson, Walker, Dunlop, McGowan, Scott, Ferguson, Smith (Prunty 65), Lister, Byrne (Taggart 65). Subs Not Used: Sandison, Noble, Motion.
Booked: McClune, Ferguson.
Goals: Walker 20.
Stenhousemuir: McCluskey, Lyle, Thom, Devlin, Dickson, Anderson (Gilmuir 86), Iain Thomson, Paton, Murray, Love (Dalziel 56), Lynch (Hunter 89). Subs Not Used: Brown, Sloane.
Goals: Anderson 57, Paton 61.
Ref: Bobby Madden
Source: BBC Sport