Wayne Corden, the only local-born player in the First Division stragglers' line-up, had stunned Arsenal by equalising with just six minutes of the additional half hour remaining. His goal, driven in from Gareth Ainsworth's cross, cancelled out Dennis Bergkamp's brilliantly chipped effort from 25 yards in the 100th minute.
Arsenal's victory came at a price, however. Ian Wright, acquainting himself with Burslem when he might have been with Benfica, limped off with a hamstring injury shortly after seeing Paul Musselwhite turn his shot on to a post 10 minutes from the end of normal time. Wright will be out for three weeks.
On the balance of play over two gruelling games, Arsenal just about deserved their success. Vale, lacking confidence after seven consecutive League defeats, had been all too content merely to hold their illustrious visitors and hope to steal something on the break.
John Rudge had opted to play the diminutive Tony Naylor as a lone striker against Steve Bould and Martin Keown, so it was hardly surprising that the better chances initially went to Arsenal. From an eighth-minute corner by Stephen Hughes, Ray Parlour saw his header cleared off the line by Stewart Talbot. Bergkamp then unleashed a long-range free-kick, but Musselwhite made a fine diving catch.
Another effort by Parlour, a shot which Musselwhite scrambled behind, appeared to confirm Arsenal's growing ascendancy. Instead, Vale should have gone ahead after 35 minutes. Andy Hill's rampaging run, fed by Ainsworth, ended with the full-back finding Naylor 10 yards out. Skipping past Dixon, the striker contrived to fire wide.
Vale promptly forced their first corner. When it was cleared, Bergkamp released Marc Overmars to run at a stretched defence. The winger's shot beat Musselwhite only to strike the inside of one post, roll along the line and pass the other.
The pitch gradually cut up, though it was a far cry from the quagmire on which Vale beat Spurs 10 years ago. Early in the second half, Bergkamp again sent Overmars scampering away. The resultant cross evaded a strangely subdued Wright and Vale breathed again.
After surviving some late scares, Vale threw on Lee Mills, and were holding their own in extra time until Bergkamp intervened. The Dutchman's first goal since mid-November was another masterpiece to add to an already impressive collection.
Vale's spirited retaliation belied their recent travails. They earned a chance to emulate Bolton, Millwall, Sheffield United and Leeds over the past four years by ending Arsenal's interest in the competition early. But Seaman stood firm, and Tankard's cup of despair overflowed.
Port Vale (4-4-1-1): Musselwhite; Hill, Aspin, Snijders, Tankard; Ainsworth, Bogie, Porter, Corden; Talbot (Foyle, 101); Naylor (Mills, 87). Substitutes not used: Glover, Stokes, Van Heusden (gk).
Arsenal (4-4-2): Seaman; Dixon, Keown, Bould, Winterburn; Parlour, Vieira (Grimandi, 75), Hughes, Overmars (Boa Morte, 90); Bergkamp, Wright (Anelka, 85). Substitutes not used: Upson, Manninger (gk).
Referee: N Barry (Scunthorpe).