East Fife almost drew level immediately when Paul McManus headed against the crossbar from six yards.
However, Young hit home a low shot three minutes from time to seal a draw for the Methil side.
Stenhousemuir: McCluskey, Gibb, Lyle, McLeod, Thom, Love (Hunter 89), Darren Smith, Iain Thomson, Motion, Dalziel, Diack (Quinn 65). Subs Not Used: Bennett, Peebles, Dickson.
Booked: Motion.
Goals: McLeod 8.
East Fife: Brown, Lowing, Robert Campbell (Conway 88), Muir, Nugent, Crawford (Cargill 80), Fagan (Linn 69), Murdoch, Young, McManus, McCunnie. Subs Not Used: Baillie, Kerr.
Booked: Murdoch.
Goals: Young 87.
Attendance: 476
Referee: S Conroy
Source: BBC Sport
Source: BBC Sport