It took some time for this play-off to stir the crowd but the home support were alarmed that it was Peterhead who nearly opened the scoring, Bobby Linn's low drive being deflected for a corner.
From Jamie Buchan's kick, Craig Tully had a shot blocked by Stewart Greacen and Kevin Nicol was similarly denied by Jim McAlistair.
Andy McLaren gave the nervous crowd some optimism when his pass found Derek Lilley on the edge of the box but the striker's subsequent pass to Chris Miller resulted only in a weak shot which was easily gathered by Paul Mathers.
Mathers fumbled a Peter Weatherson free-kick but he recovered well to knock the ball for a corner as Ryan Harding bore down to convert the rebound. The Blue Toon keeper comfortably held a McLaren chip but Morton were failing to put their visitors under any sustained pressure.
Just before half-time Peterhead, sparked by the lively Graeme Sharp, looked certain to open the scoring but first, David McGregor, and then Alex Walker intervened to make the half-time score goalless.
After the break Morton failed to impose themselves and Peterhead looked the more likely to score. Tully, moving on to a clever Sharp pass behind the Morton rearguard, forced David McGurn into a desperate save. Tully, under pressure from McGurn, knocked the rebound wide.
Mathers had an anxious moment when Tully attempted to clear a Morton cross with his chest but he only succeeded in striking the base of his post. There were no other scoring attempts worthy of description.