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Pope hit the crossbar and was denied by a fine Ryan Clarke save early in the game, as Vale stormed out of the blocks.
The breakthrough came on 30 minutes when the 27-year-old forward tapped home from close range, after Ashley Williams's shot had been parried by the frequently-exposed Clarke.
Vincent doubled the hosts' lead six minutes into the second half with an audacious effort from an extremely narrow angle.
Morsy was a little fortunate to remain on the pitch when his poorly-timed tackle on Jake Forster-Caskey was punished with only a yellow card just before the hour-mark.
However, the combative midfielder regained his composure and completed the scoring moments later with a stunning 25-yard strike.