Taylor, who rejoined Vale ahead of kick-off, set up Sam Foley and scored one himself before Louis Dodds pulled one back for the visitors, leaving the Valiants just two points off both Town and Oldham.
After a tightly contested first-half, the hosts took the lead on 66 minutes when Taylor whipped in a corner for Foley to plant a header into the net.
Vale doubled their advantage just three minutes later when Kiko broke down the left and put in a low ball across the box to Taylor, who slotted home past Jayson Leutwiler from 10 yards out.
Shrewsbury reduced the deficit after 74 minutes when Dodds, who spent eight years at Vale Park, fired an unstoppable 20-yard shot past keeper Deniz Mehmet.
But Dodds' goal wasn't enough for Town as Vale held on, through a nervy closing period, for what could be a vital three points in their fight for survival.