After Daryll Meggatt had shocked the visitors with a fortunate opener, Liam Craig and David Gray were on target as Hibs avenged their Scottish Championship defeat from earlier in the season.
However, the Edinburgh giants had to finish the game with just 10 men after Dominique Malonga was sent off three minutes from time.
After being out-played during the opening stages, Alloa took the lead against the run of play with Meggatt finding the bottom left-hand corner of the net from outside the box in the 15th minute.
Yet his long range effort should have been stopped by keeper Mark Oxley who allowed the ball to run through his legs.
And as Hibs chased an equaliser, Gray headed narrowly wide on 22, with the visitors finally getting the goal they deserved six minutes later.
After Mark Cawley was penalised for handball, Craig curled home the resulting free-kick into the bottom corner.
Nine minutes before the break the dominant visitors duly went ahead as Gray met Scott Allan’s cross at the far post to score with a looping header.
But with 87 minutes on the clock, Malonga saw red for violent conduct, following an off the ball incident.