McGurk's first goal of the season capped a solid away performance by Rovers, who created far more chances than their struggling opponents.
Tranmere could have led inside the first two minutes, Jake Jervis slicing off target from McGurk's low cross.
Oldham went close when Dean Furman forced a last-ditch clearance from Ash Taylor, while Jose Baxter also threatened for the Latics as he shot inches wide from 20 yards.
Visiting goalkeeper Owain Fon Williams did well to deny Cristian Montano, but the visitors wasted two great chances before half-time as James Wallace missed from six yards and Jake Cassidy failed to hit the target when clean through.
Tranmere went ahead after 54 minutes as Jervis crossed from the left and McGurk steered home a far-post volley from eight yards. Oldham created little until stoppage time when Fon Williams saved smartly from Youssouf M'Changama's 20-yard blast.