Pope, Vale's leading scorer as Micky Adams' men won promotion last season, struck in the 63rd minute as the Valiants came from behind to win all three points.
Danny Kedwell had put the visitors in from early on but Chris Robertson equalised at the beginning of the second half.
Both sides threatened in a very open start to the game before Gillingham took the lead in the 13th minute.
Amine Linganzi did well to dig out a cross from the left byline and Kedwell made no mistake with a far-post header from just four yards out.
Vale tried to hit back with Ben Williamson, Carl Dickinson and Doug Loft all going close to an equaliser before the end of an entertaining first half.
But they levelled just two minutes after the interval when Chris Lines' right-wing corner was flicked on by Dickinson for Robertson to bury a close-range header.
A Vale onslaught followed and it was no surprise when Pope, who replaced youngster Jordan Hugill at half-time, gave them the lead.
Dickinson lofted the ball into the right side of the Gillingham penalty area and Pope's header flicked the inside of the right-hand post on its way into the back of the net.