The first half was a generally poor affair with few clear-cut chances, with Port Vale perhaps shading it in terms of possession as the breakthrough came five minutes before the interval.
Exeter felt they should have had a free-kick on halfway, but the referee played an advantage which was not there. City's attack broke down, Jennison Myrie-Williams took full advantage and crossed to the far post for Pope to head in from six yards.
Exeter thought they had equalised when Danny Coles crossed into the box, but Steve Tully's powerful header hot the top of the crossbar.
And Vale made the Grecians pay as Ashley Vincent crossed for Pope to nod his second shortly past the hour mark.
With the points safely in the bag Vale were happy to sit back and let Exeter have the ball, with Guillem Bauza's long-range shot which was saved by Chris Neal the best they could manage.