For much of the first half a home victory looked on the cards for the home side after taking an early lead at Recreation Park.
There was not a lot of action in the opening stages and home pressure paid off in the 13th minute when Shipyard were awarded a penalty after Peebles keeper Chris Malcolm brought Adam Doig down in the box. The same man gained revenge by slotting the resultant spot kick past the visiting No 1.
The first half came to an end with Peebles yet to record an attempt on target and the home team looking comfortable.
Whatever was said or done in the Peebles dressing room at half-time certainly had the desired effect.
In the 53rd minute Shipyard keeper Jordan Mushet produced a fine double save as Peebles looked for an equaliser.
The goal came two minutes later following a lapse in the Shipyard defence. A free-kick was punted into the box and Mushet hesitated after calling for the ball, allowing Chris Flockhart a free header inside the six-yard box.
The visitors were now dominating the match while Shipyard struggled to put two passes together.
Peebles took the lead when a through-ball that should have been cut out wasn’t, allowing substitute Sean Meikle to break into the box and beat Mushet with a finely-struck angled drive.
The hosts huffed and puffed in the final few minutes and despite Peebles being reduced to 10 men when Greg Shortreed received a second yellow card for a cynical trip on Craig Lowe, Malcolm was never threatened as his side held on quite easily.