The youngsters remained unbeaten in their League Cup qualification group with a narrow win over the Wasps at Beath High School on Sunday afternoon.
Dale Finnie opened the scoring after 19 minutes when he headed home from a Callaghan corner.
However Alloa drew level just four minutes later when Ben Anthony shot past Wilson from close range.
Cowden however restored their lead three minutes into the second half when Craig Johnstone shot home from close range.
Once again the Wasps quickly drew level sixty seconds later with Anthony once again on target.
With 67 minutes gone Nicholson was brought down in the box and Liam Callaghan fired home the resultant spot kick.
Alloa once again equalised within a minute when Greig Smith shot home from seven yards, however Finnie secured the points with 16 minutes to go with a close range effort after the keeper failed to hold a Callaghan free kick.