Striker Jack Midson's double had given the hosts a two-goal cushion but goals either side of the break from debutant Daniel Jones and Pope extended Vale's lead at the top of the table to two points.
The Dons, needing a win to leapfrog Plymouth into 22nd, went ahead after eight minutes. Jim Fenlon crossed for Midson who swept the ball home from eight yards.
Vale, who had won four of their previous five games, then came close through Ryan Burge who tested 42-year-old Neil Sullivan's reflexes.
But, in the 42nd minute, Liam Chilvers dragged down Pim Balkestein in the box and Midson struck home the resulting penalty.
Port Vale responded immediately, though, with defender Jones firing home from 35 yards into Sullivan's bottom corner.
And the league's top scorer Pope then notched his 27th goal of the season just before the hour, latching on to Mat Mitchel-King's short backpass, rounding Sullivan and slotting home from a tight angle.
- Sports & Recreation
- Neil Sullivan
- Jack Midson