They dominated throughout the game and should have won more comprehensively had they taken more of the many chances they created.
Peterhead took a sixth minute lead, Alloa defender Michael Bolochoweckyj pushing Iain Good, and Dougie Cameron sent the spot-kick low into the left corner.
The Blue Toon should have increased their lead. Graeme Sharp saw a header saved then failed to capitalise after Alloa keeper Allan Creer dropped a cross from the left wing. Martin Bavidge had a volley saved by Creer at the expense of a corner, but Peterhead eventually did increase their lead six minutes into the second half.
It was a slip by Bolochoweckyj, allowing Martin Wood to pounce and take the ball around Creer before sliding his shot into the net.
Soon after the second goal Sharp should have scored, but with only the keeper to beat he shot wide of the right-hand post.
It was 3-0 after 63 minutes, Kevin Nicol heading the ball on to to Bavidge, and he drove into the penalty area before sending a shot into the far corner of the net.
Alloa had the chance to score a consolation goal after 75 minutes but James Stevenson saw his penalty saved by home keeper Paul Mathers, rounding off a day the visitors will want to forget.