Jim McInally’s men went into the match looking to bounce back from their 2-1 loss at Queen’s Park last Tuesday.
But they were up against it early on as Cove struck twice on the opening 10 minutes.
The first came in eight minutes and was controversial as referee Gavin Duncan pointed to the penalty spot, judging that Blue Toon skipper Scott Brown had tripped Harry Milne.
The visitors were far from happy but the award stood and former Blue Toon icon Rory McAllister netted from 12 yards to put the hosts in front.
Cove doubled their advantage just two minutes later. Fraser Fyvie opened up the Peterhead backline with a through ball which allowed Mitch Megginson to run clear, round Brett Long and knock the ball into an empty net.
It looked like being a long afternoon for Peterhead but they tried to respond quickly and Hamish Ritchie fired in a decent effort from the edge of the box which was only just too high.
But it wasn’t to be long before Ritchie, who had a loan spell with Cove in 2020 before he joined Peterhead, did find the target.
On 15 minutes the Blue Toon man picked up the ball at the edge of the box and hammered it past Stuart McKenzie to get his side back in the game.
However it was to be a brief respite.
Just six minutes later Milne’s cross was met by Megginson who blasted the ball past Long to restore Cove’s two-goal advantage.
Megginson was denied a hat-trick by a Long save while at other end Andy McDonald sent an effort wide of goal and Grant Savoury saw a shot kept out by McKenzie.
McAllister fired wide just before half-time and it remained 3-1 at the interval.
At that stage it was clear whoever got the next goal of the match would prove crucial – and unfortunately for Peterhead it was Cove who struck just two minutes into the second half as Blair Yule’s past set up the opening for Milne to slot the ball last Long from six yards.
It was a long way back for Peterhead and it could have got worse as Mark Reynolds fired over from the edge of the box and Conor Scully saw a lob hit the top of the bar.
McDonald did bring McKenzie into action with a well-struck shot which the Cove keeper did well to hold.
But Peterhead fell further behind on 76 minutes when Megginson set up Milne to shoot into the bottom corner.
All told it was an afternoon for Peterhead to forget, but there was some brightness among the gloom with the return after a serious knee injury of Gary Fraser who was sent on to replace Scott Brown for his first appearance in nearly 15 months.
And the visitors did have the final say in terms of the afternoon’s goals seven minutes from the end as Russell McLean charged down McKenzie’s hastily forced clearance from a short Reynolds passback and then ran through to drive the ball into the empty net.
But it was too little, too late