Elgin were beaten for the third consecutive game as Peterhead recorded a 3-0 win in the all-Highland clash at Borough Briggs.
Stuart Leslie missed a good early chance for City when he steered his left-footed effort wide from close range.
Alloa loanee David Cox made no mistake at the other end, finding the top corner in the 19th minute from the edge of the area after a prolonged spell of Blue Toon pressure.
Ryan Strachan's long-range free-kick extended the visitors' lead seven minutes before the interval.
Leslie continued to pose an attacking threat and almost brought the Black and Whites back into the game, but Graeme Smith was equal to his 71st-minute drive.
Jim McInally's men put the result beyond doubt 15 minutes from time when Robbie Winters swept home Scott McLaughlin's pass.