The visitors tested the nerve of the home side after six minutes when Kyle Perry headed Mark Branch's corner towards goal but striker Dean Perrow couldn't connect with the ball.
A foul by John Branch on Callum Willock invited Luke Rodgers to try a free-kick in the 18th minute and he didn't disappoint by sending his 25-yard effort into Lee Evans' top left corner.
After little from both sides during the first half, Rodgers carved out a shooting opportunity for Danny Whitaker two minutes before the break but his 12 yard shot flew over the crossbar.
Chasetown got their dream equaliser a minute later when some lacklustre defending allowed Mark Branch's 40-yard free-kick to creep through the box and into Joe Anyon's goal.
The opening stages of the second half saw little improvement from Vale with another free-kick from goalscorer Mark Branch setting up Vaughan Thomas for a header that he put onto the roof of the net.
As Lee Sinnott's men struggled to break down a brave Town defence, it was left to Justin Miller to try his luck from distance in the 59th minute but his effort fell wide of the goalkeeper's left post.
Things looked to be going in the right direction for Vale but they still struggled to find the target despite Ashley Westwood sending a looping header inches over the crossbar.
As the game entered the last couple of minutes, the opportunity for a replay on home turf became a real prospect for Chasetown thanks to a lack of creativity from the Valiants.
The final whistle saw jubilant celebrations from the 2,000 away supporters, but it was the angry demonstration from the Port Vale supporters that soured the mood with a small group venturing onto the pitch to remonstrate with the exhausted players.