The hosts started the stronger and in the seventh minute saw a great opportunity wasted when Michael Bolochoweckyj, who was just four yards out, headed past the post rather than into the open goal.
Two minutes later, however, it was Alloa goalkeeper Gary McGlynn who saved his side by pulling off a wonderful save, when he turned away a fierce Dougie Cameron shot.
In the 20th minute Peterhead suffered a severe blow when they lost the services of striker Bobby Linn with a severe leg injury.
Just before the break Alloa came close to breaking the deadlock, but Bolochoweckyj, who had beaten the offside trap and ran onto a James Stevenson pass, made a poor connection and his shot dribbled wide.
Against the run of play Peterhead took the lead in the 62nd minute when substitute Scott Michie scored from the penalty spot.
The spot-kick was awarded after Chris Townsley fouled Graeme Sharp. In the melee that followed Townsley was shown a straight red card by referee Boyle.
Alloa were thrown a lifeline in the 72nd minute when they were awarded a penalty after Cameron brought down Jose Quitongo on the edge of the box.
However, Stevenson's kick was brilliantly saved by Paul Mathers in the Peterhead goal.
Michie scored his second of the day in the 89th minute when he ran onto a defensive clearance and from 25 yards out, fired the ball home.