The Glasgow side got off to a flying start - debutant Nicky Clark taking less than a minute to open his account for his new club when he raced on to McCulloch's flick-on and slotted home.
McCulloch had already seen one decent chance flash wide when he netted his first on 17 minutes with a neat glancing header past East Fife goalkeeper Michael Andrews.
The crossing ability of Lee Wallace was causing the visiting defence all sorts of problems and it was another accurate delivery that provided McCulloch with a routine headed finish before half-time for his second of the afternoon.
Arguably the goal of the match came from Lewis Macleod shortly after the break - his searing 20-yard volley finding the corner and leaving Andrews with no chance.
Fittingly, however, the last word went to McCulloch, who completed his trio of headers with yet another assured connection - this time converting a cross from Kyle McAusland shortly after the hour mark.