Derek McInnes rang the changes from the Dons' Europa League hammering of Daugava Riga in the first-round, first-leg game.
Aberdeen dominated for chunks but Peterhead twice went close after the interval through a 50-yard effort from new signing Jamie Stevenson and a hooked Rory McAllister effort.
Lawrence Shankland scored just after the hour with a scruffy shot that sneaked inside the far post from Cammy Smith’s cross.
Source: The Daily Record