Two late goals capped a splendid fight-back by 'Ton and preserved their lead over next weeks' opponents, Stirling .
David McGregor created the first chance with a cross which eluded everyone and fell to Jamie Stevenson but the ex-Alloa man failed to control the ball and The Blue Toon took full advantage, Keith Gibson picking out Martin Bavidge in the box, allowing the striker to thrash a rising angular shot past a startled David McGurn.
Bavidge was troubling the Morton defenders and Weatherson had to make a last-ditch tackle to deny him converting a Steve McNally cross.
Startled 'Ton replied with a Chris Millar drive from Ryan Harding's knock-down which flew wide and a smart move which played in Paul McGowan only for Craig Tully to make an excellent saving tackle. Harding, however, clumsily conceded a corner and Tully powered in a header from Graeme Sharpe's kick despite Jim McAlister's attempt to punch the ball out.
McGowan gave the home support hope when he pulled one back, volleying past Greg Kelly after Peter Weatherson's direct incursion into the Peterhead penalty box. Weatherson himself equalised, heading in Stevenson's corner.
Peterhead withstood stoutly wave after wave of attacks and looked like giving new boss, Steve Paterson, a point but, with two minutes to go, Scott McLaughlin volleyed in a clearance from a corner from twenty-five yards and Kevin Finlayson headed in a Millar cross.
Paterson admitted that his players were overrun in the second half, his counterpart, Jim McInally, glowing with admiration at his side's resilience.