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.
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.