Peterhead bounced back from a defeat at the hands of Stranraer last week to take a vital three points at Morton.
Morton should have gone in front early on when Jon Sucllion sent Rickie Lamie down the left and his cross from Jamie McCluskey, but he missed an open goal.
Peterhead went on the attack and created an opening when Stevenson swung over a corner on the left but Rory Mcallister’s header was well held by keeper Gaston.
It was end-to-end action throughout the first half as both teams headed for the dressing room goalless at the end of 45 minutes.
However, Blue Toon fans were on their feet just 11 seconds into the second period when Jamie Stevenson darted down the left and cut inside and drilled the ball low into the back of the net to give the visitors the lead.
Just two minutes later Stevenson was denied a second when Gaston was forced to make another superb save.
The match ended with all three points heading to Balmoor, much to the delight of Blue Toon boss Jim McInally.
Speaking after the game he said his side had defended really well throughout the match but now had to concentrate on winning home games.
“On our day we are as good as any team in the league,” he said.
“We’ve just got to start to do better at home, which is usually a fortress.
“I don’t think our goalkeeper had a save to make all match. We really broke well and McAllister had a purple patch.
“He became a father last week and wasn’t at his best for the Stranraer game, but he looked more like himself today,” he said.
The focus now turns to the next game when Peterhead will take on Forfar at Balmoor on Saturday.
With Forfar currently sitting in second place, it’s another hard match for McInally’s side.
Meanwhile, the January transfer window is fast approaching and McInally has already two targets in mind in a bid to boost the Blue Toon’s promotion hopes.
“It is possible that Ritchie Ryan will come in for a couple of months, while we are also trying to get Nicky Riley.
“He’s quite sought after but has been training with us, while Ritchie is playing in Canada just now, so it would be a short-term loan” added McInally.