This eagerly awaited north east derby started at cup tie pace and it was the home side who threatened first in the fouth minute.
Some neat footwork on the left side of the penalty area by Rory McAllister found Scott Brown who fired over from 12 yards.
Back came Cove and six minutes later Mitch Megginson broke clear after cashing in on a slip by Cameron Eadie and his cross picked out Jordan Brown who was denied by Greg Fleming diving low to his right.
But after 14 minutes it was advantage Cove.
A Megginson shot at ground level was handled by Jason Brown and Jamie Masson smashed home the spot kick giving Fleming no chance.
Peterhead were level after 21 minutes though, an outswing corner from the left by Jack Leitch and a downward header at the back post by Derek Lyle.
The Blue Toon should have taken a lead into the break with McAllister racing clear but his shot was stopped on the line in spectacular fashion by Harry Milne.
They weren’t to be denied though as we had our second penalty of the half, McAllister being chopped to the ground by Darryn Kelly with the striker doing the needful himself from the spot.
We almost had a stunning start to the second half, Cove’s Milne whipping over what was surely a cross from the left wing but ended up crashing off the face of the crossbar.
Five minutes later, unbelievably, Milne did it again this time with a shot from closer range hitting the woodwork.
The visitors continued to look more likely to score again and a slide rule pass forward by Connor Scully into the area saw Blair Yule fire the ball low just beyond the far post.
A Lyle header following a corner kick that faded wide as the match headed towards its conclusion was a rare attacking threat from the home side in the second half.
Peterhead will have their second match of the group tonight (Tuesday, July 16) as they host Championship side Inverness Caledonian Thistle at Balmoor ahead of a trip to Dundee FC on Saturday.