Town also ended the game with ten men following the late dismissal of substitute Marc Pugh, but will be kicking themselves for not turning possession into goals.
The day started well for Vale when young striker Steve Thompson gave them the lead with a stunning goal in the ninth minute.
Thompson, an ex-Middlesbrough trainee, cut in from the right flank and hammered an unstoppable 25-yard shot which tore into the top corner of the net.
Shrewsbury were bossing most of the play, however, and were full value for Richard Walker's 27th minute equaliser.
Walker benefited from some less than convincing Vale defending to fire in a close-range shot which struck Vale keeper Joe Anyon and looped into the net.
Shrewsbury were given a helping hand five minutes later when Perry was adjudged to have elbowed his marker Kelvin Langmead in the face.
Perry and his team-mates protested the player's innocence, but referee Trevor Kettle was adamant and he was sent to the dressing room.
Vale did well to hold firm under strong pressure until half-time and almost grabbed an unlikely lead when Thompson's header was held by Luke Daniels.
Shrewsbury huffed and puffed without seriously threatening a breakthrough and manager Paul Simpson introduced Nick Chadwick and Pugh to lift his troops.
But Pugh had only been on the field for three minutes when he saw red for a high challenge on Vale full-back Anthony Griffith in the 74th minute.
Both teams tried to win the game in the closing stages but a draw was a fair result.