The visitors failed to make the most of their early chances and had to be alive to the home side's lively attackers on a number of occasions, eventually conceding goals to Liam Buchanan and Iain Flannigan after half-time to fall to another disappointing reverse.
Alan Stubbs' men have only three points after four games and already find themselves nine points adrift of fierce Edinburgh rivals Hearts, who have won their first four.
Hibs took the lead on 14 minutes when, after Farid El Alagui headed just wide, Jason Cummings climbed to head home Sam Stanton’s corner.
The visitors appeared to be well in control but then had a couple of scares midway through the first-half when Jordon Forster made a brave block and Mark Oxley a fingertip save to deny Kevin Cawley an equaliser.
Oxley was again called into action on 33 minutes when Ryan McCord fired in a long-range effort the Hibs keeper had to deal with.
Hibs suffered a blow just before the break when the influential El Alagui was stretchered off after appearing to suffer what could be a serious ankle injury.
Cummings spurned a glorious chance to double his tally and make it 2-0 early in the second period but soon after Alloa were level, Buchanan pouncing to score in the 57th minute after Oxley failed to hold a shot.
Forster went close to grabbing the lead back for Hibs with a volley just off target, but it was the Wasps who grabbed the points with a goal six minutes from time, a sensational free-kick from Flannigan ending up in the top corner of Oxley's net.