Gillingham took the lead through Danny Kedwell's far-post header, but Chris Robertson equalised for the home side with a close-range header.
Vale mounted pressure after the interval and it was no surprise when half-time substitute Pope headed home in the 63rd minute.
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Sunny this evening, then dry overnight. There is the risk of thundery showers for Kent tomorrow morning, then sunny spells by the afternoon
Sunshine to end the day then dry tonight. Tomorrow will be mostly dry and feeling fresher with the risk of a heavy shower in the afternoon
The video, obtained by ITV News, shows scores of migrants desperately trying to board lorries in a restricted area within the tunnel.