The game struggled to come to life in the first-half as neither side managed to produce a meaningful attempt on goal.
A livelier affair after the restart, both sides had chances before Tom Pope notched the opener just past the hour-mark.
Looking like being the difference between the two teams, Jordan Green popped up in the 89th minute to earn the visitors a replay and keep Town in the pot for the third round draw.
Darren Way made two changes from last weekend’s league outing, including a fifth start in Green and White for Alefe Santos.
Impressing in midweek, the Brazilian replaced Matt Worthington in midfield whilst Otis Khan – who returned from illness on Tuesday night – came in for Jordan Green.
New signing Oscar Gobern started amongst the substitutes after signing on Friday morning following a three-week trial.
On a drizzly afternoon in Staffordshire, the opening 45 minutes failed to provide much in terms of final third action as both sides cancelled each other out.
Neil Aspin’s side were first to enjoy a spell of pressure, but despite a string of balls into the box the Valiants were unable to test Artur Krysiak.
Growing into the match, Santos started to control proceedings in midfield for the visitors as the momentum swung in favour of Town.
However, much like the home side, the Glovers were unable to bring the opposing ‘keeper into play as James Bailey’s blocked shot from inside the box proved to be Yeovil’s best chance of the half.
With frustration growing amongst both sets of supporters the game continued to struggle to produce attempts on goal, with Christian Montano twice off target with efforts 18 yards.
As two minutes of additional time came to a close Port Vale engineered the best chance of the half as Gavin Gunning’s deep cross found Pope, whose goalbound header was manfully blocked by Omar Sowunmi.
That brought an end to a first-half that largely failed to inspire, leaving plenty of food for thought for both sides at the break.
Whilst Town chose to stick with the eleven that started at Vale Park, the Valiants opted to twist with a double substitution and change in formation at the start of the second half.
Now with two up front, the alterations gave the Yeovil defence food for thought as Anton Forrester had a header from 12 yards claimed by Krysiak.
Staying in the ascendancy after the restart, Vale squandered their best two chances of the match as the game ticked towards the hour-mark.
Firstly, Pope had a shot from inside the box blocked by his own man after substitute Tyler Denton raced clear, before a last-ditch Ryan Dickson challenge stopped Forrester pulling the trigger from six yards after Krysiak was taken out of the game having got a hand to a deep cross.
Living dangerously, the Glovers survived the flurry of Port Vale chances and almost broke the deadlock themselves.
Great work from Sam Surridge saw the striker weave his way into the box before unselfishly squaring for Khan, whose low drive was deflected inches wide.
However, Aspin’s side responded immediately and opened the scoring after 63 minutes.
A hanging cross to the back post was perfect for Valiants top scorer Pope to rise highest and head past a hapless Krysiak.
The game’s opening goal sparked a double change from Way, as Gobern – making his debut – and Green took to the field in place of Bailey and Khan.
Despite the fresh legs, it was Vale who continued to enjoy the most of possession as time suddenly became the enemy of the Green and Whites.
Forrester missed an opportunity to put the tie beyond doubt inside the final ten minutes before Town ensured they’d be in the hat for the third round draw.
Gobern’s cross fell to Green in the box who made no mistake in heading the ball into the back of the net for his first Yeovil goal to send the away end into raptures.
The visitors searched for a winner in stoppage time buoyed by the equaliser, but the referee’s whistle brought an end to proceedings forcing a replay at Huish Park in a few weeks’ time.
Port Vale: Boot; Gibbons, Gunning, Anderson, N. Smith; Tonge, Kay, Pugh (Denton 45′); Worrall (Harness 72′), Pope, Montano (Forrester 45′).
Bookings: Gibbons 87′
Subs not used: Hornby, Barnett, Reeves, Turner.
Yeovil Town: Krysiak; James, Sowunmi, N. Smith, Dickson; Bailey (Gobern 69′), Santos (C. Smith 82′); Olomola, Zoko, Khan (Green 69′); Surridge.
Bookings: Dickson 32’
Subs not used: Maddison, Mugabi, Davies, Worthington.