Taylor, who re-signed on Friday after previously leaving Vale at the end of a short-term deal earlier this term, set up Sam Foley and scored one himself to earn Vale's second straight home win.
Louis Dodds netted a consolation for the visitors but there was no way back.
Vale remain in the drop zone but are now just two points below Shrewsbury.
The hosts, who still have two games in hand on their relegation rivals, scored twice in the space of three minutes as Foley headed in Taylor's corner before the former Newcastle man turned in Kiko's square ball.
Former Vale player Dodds' long-range strike was not enough to prevent the visitors losing for a third time in four away games.
Match ends, Port Vale 2, Shrewsbury Town 1.
Second Half ends, Port Vale 2, Shrewsbury Town 1.
Corner,  Port Vale. Conceded by Mat Sadler.
Nathan Smith (Port Vale) wins a free kick in the attacking half.
Foul by Aristote Nsiala (Shrewsbury Town).
JJ Hooper (Port Vale) wins a free kick in the attacking half.
Foul by Aristote Nsiala (Shrewsbury Town).
Attempt missed. A-Jay Leitch-Smith (Shrewsbury Town) header from the centre of the box is close, but misses to the right.
Attempt missed. Dan Turner (Port Vale) right footed shot from the centre of the box is too high.
Substitution, Shrewsbury Town. A-Jay Leitch-Smith replaces Joe Riley.
Ryan Taylor (Port Vale) is shown the yellow card for a bad foul.
Foul by Ryan Taylor (Port Vale).
Louis Dodds (Shrewsbury Town) wins a free kick in the defensive half.
Attempt saved. Tyler Roberts (Shrewsbury Town) right footed shot from outside the box is saved in the centre of the goal.
Foul by Sam Kelly (Port Vale).
Gary Deegan (Shrewsbury Town) wins a free kick in the defensive half.
Foul by Sam Kelly (Port Vale).
Junior Brown (Shrewsbury Town) wins a free kick on the left wing.
Stephen Humphrys (Shrewsbury Town) is shown the yellow card for a bad foul.
Sam Kelly (Port Vale) wins a free kick in the attacking half.
Foul by Stephen Humphrys (Shrewsbury Town).
Substitution, Port Vale. Sam Kelly replaces Chris Eagles.
Foul by Ryan Taylor (Port Vale).
Junior Brown (Shrewsbury Town) wins a free kick in the defensive half.
Nathan Smith (Port Vale) wins a free kick in the attacking half.
Foul by Stephen Humphrys (Shrewsbury Town).
Attempt blocked. Tyler Roberts (Shrewsbury Town) right footed shot from a difficult angle on the right is blocked.
Corner,  Shrewsbury Town. Conceded by Remie Streete.
Attempt blocked. Tyler Roberts (Shrewsbury Town) header from the centre of the box is blocked.
Corner,  Shrewsbury Town. Conceded by Remie Streete.
Attempt blocked. Tyler Roberts (Shrewsbury Town) right footed shot from the left side of the box is blocked.
Attempt saved. Junior Brown (Shrewsbury Town) right footed shot from the left side of the box is saved in the centre of the goal.
Goal!  Port Vale 2, Shrewsbury Town 1. Louis Dodds (Shrewsbury Town) right footed shot from outside the box to the top right corner. Assisted by Stephen Humphrys.
Corner,  Shrewsbury Town. Conceded by William Reeves.
Attempt blocked. Joe Riley (Shrewsbury Town) right footed shot from outside the box is blocked.
Foul by Ryan Taylor (Port Vale).
Junior Brown (Shrewsbury Town) wins a free kick on the left wing.
Ryan Taylor (Port Vale) wins a free kick on the right wing.
Foul by Junior Brown (Shrewsbury Town).
Substitution, Shrewsbury Town. Stephen Humphrys replaces Stefan Payne.
Port Vale boosted their League One survival hopes as a goal and an assist from returning defender Ryan Taylor saw off fellow strugglers Shrewsbury Town.