The Skrill Premier side threatened to cause an upset on home soil on Friday night until Pope rose to bury a downward header from 10 yards after Taylor crossed from the left in the 78th minute.
And Pope soon returned the compliment with a clever pass which gave substitute Taylor the space to place a 14-yard right-foot shot just inside Will Puddy's left-hand post.
Salisbury held their own for much of the first half, though, and were unfortunate to trail at the break when Chris Robertson fired in a low left-foot drive from 10 yards after Pope's effort was deflected into his path.
And the visitors deserved their 64th-minute equaliser when Vale failed to clear Elliott Frear's free-kick from the left flank and Dan Fitchett forced the ball in from point-blank range after his initial effort was saved by Vale keeper Sam Johnson.
The hosts' substitute Ben Williamson turned smartly to fire in his side's fourth goal a minute from time as his 16-yard shot flashed low inside Puddy's left-hand post to seal the win.