With both teams wearing their change strips, it was the home side who kicked off and immediately went on the offensive.
It took a brave block by Peterhead midfielder Scott Brown on the edge of his area from opposite number Jim McAllister to stop a shot on target in the second minute.
The visitors response was almost immediate, former Morton player Jamie Stevenson with a wicked 25 yard shot that bounced just in front of Derek Gaston with the keeper scooping the ball out for a corner kick.
That chance gave the Blue Toon confidence but it was the Greenock side who looked the more dangerous powering forward and a driven cross from the right by Bob McHugh carried just a bit too much pace as it flew across the six yard box.
With 14 minutes gone the home side went even closer, a low drive well struck by Michael Tidser from the right of the six yard box but keeper Greg Fleming did well to get down and save to his right.
Moments later McHugh laid the ball off to Gary Oliver but he was denied by another fine save from Fleming.
The breakthrough came in the 28th minute and a super goal it was from the visitors.
A skilful turn out on the right wing by Ryan Dow sent the Morton left back sprawling and his low cross found Scott Brown who tucked the ball into the far corner from 12 yards.
Five minutes before the break it could have been two, Dow getting a head flick on a Willie Gibson corner that was cleared off the line but seconds later it was all square, Bob McHugh getting a touch at the near post to equalise.
It was all Peterhead from the restart with Michael Tidser clearing off the goal line as the home side looked nervous under pressure but they broke upfield and it took a third fine save of the game from Greg Fleming to stop Reghan Tumilty.
Ryan Dow, on loan from Ross County, was outstanding but he should have done better after 73 minutes cutting inside but blazing the ball high and wide from the edge of the area.
Despite the Blue Toon looking the more likely to snatch a winner it ended all square with the tie going to a replay at Balmoor Stadium on Tuesday night with the winners travelling to League 1 side East Fife in the fourth round on the weekend of January 19.