The visitors should have taken a 13th-minute lead when Tope Obadeyi fired a close-range shot against a post when it looked easier to score.
And Vale made them pay just two minutes later with the in-form Gavin Tomlin scoring for the fourth successive game.
Jennison Myrie-Williams curled over a free-kick from the left and Tomlin guided a 12-yard header low inside Jake Cole's left-hand post.
Plymouth had a mountain to climb when Tom Pope buried a 10-yard header from Doug Loft's left-wing cross in the 36th minute.
But they were right back in a pulsating clash six minutes after the break when Reuben Reid rolled the ball into an unguarded net from 12 yards after fine work by Durrell Berry and Lewis Alessandra.
And Alessandra also played the vital pass before substitute Ben Purrington squeezed a low left-foot shot inside Chris Neal's left-hand post from the corner of the six-yard box for a 73rd-minute equaliser.
It was all Plymouth in the closing stages and Andres Gurrieri was inches away from a winner in the last minute of normal time when his 20-yard shot crashed against Neal's right-hand post.
|Team Name||Port Vale||Plymouth Argyle|
|Shots On Target||4||5|
|Shots Off Target||0||8|