Neale Cooper's men levelled five minutes later through Nicky Clark's close range strike.
However, Peterhead's Paul Emslie saw red for violent conduct before half-time and Callum MacDonald's own goal on 79 minutes sealed Alloa's win.
Alloa: Crawford, McClune, Walker, Townsley, Buist (Gilhaney 46), Carroll, Grant, Brown, Noble, Prunty (Gormley 88), Scott. Subs Not Used: Flynn, Hay, Brown Ferguson.
Goals: Noble 29, MacDonald 79 og.
Peterhead: Jarvie, Donald (MacDonald 51), Mann, Crawford, Stuart Smith, Barry Wilson, McVitie (Emslie 33), Clark (Sharp 81), Strachan, Bavidge, Ross. Subs Not Used: Keiran Wilson, Gethans.
Sent Off: Emslie (40).
Booked: Crawford, Mann, Strachan.
Goals: Clark 34.
Attendance: 448
Referee: C Charleston.
Source: BBC Sport
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