Brechin City had to make a number of changes to their side for the clash against Peterhead.
Paul McLean and Craig Molloy were both suspended, and Gary Fusco was unavailable through illness.
Ewan McNeil replaced McLean, while Ollie Durojaiye got his first start for the club since joining from Falkirk on loan.
City threatened after just four minutes, with Robert Thomson headed effort saved by Peterhead ‘keeper Graeme Smith.
Smith was back in action moments later, this time to deny a close range effort from Andy Jackson.
Peterhead came close to scoring in the 12th minute, with Cammy Kerr’s shot pushed onto the cross bar by Graeme Smith.
Smith again was on hand to deny the homesters in the 22nd minute, this time tipping a Stevenson shot from 25 yards out over the bar.
Peterhead eventually took the lead in the 32nd minute, with Rory McAllister playing a low ball across goal which was touched in by Gary McDonald.
Hopes of a second half comeback for City were dealt a severe blow in the 63rd minute when Colin Hamilton picked up a second yellow card, reducing the visitors to 10 men.
Peterhead made the most of their advantage, and increased their lead in the 71st minute. A Stevenson freekick fell kindly to David Cox who slotted the ball into the net from six yards out.
With the their unbeaten record on the line, Brechin tried admirably to get back into the game, but with a two-goal cushion and a player more, Peterhead were able to defend their lead comfortably.
They dealt a final blow to City in injury time, when Jordan Brown side footed a Cox corner for The Toon’s third and final goal.