Alfie Devine's strike early in the second half proved enough for Vale to make the last eight of the competition and deny Stags revenge for Vale's Wembley play-off final win of two seasons back.
Stags had already knocked out Championship and League One opposition in earlier rounds, but Vale, despite poor recent league form, were the better side and deserved winners with Mansfield rarely threatening the Vale goal.
Stags had only ever reached this stage once before in 1975 and knew a Premier League big gun was likely to be the prize. But it simply wasn't to be.
Vale dominated the first half and Oliver Arblaster came closest when he hit a post while Christy Pym saved well from Tom Sang.
But Stags almost stole the lead from a Davis Keillor-Dunn volley that keeper Connor Ripley was able to block.
Vale finally broke through five minutes into the second half through a powerful low Alfie Devine shot and protected their goal perfectly afterwards.
Mansfield now prepare for another huge tie when Wrexham visit on Saturday night in the FA Cup first round.
Sadly for Stags, striker Lucas Akins was not fit enough to play as he recovers from a bang to the head at the weekend. But his absence offered a start for Will Swan against a club where he had a loan spell.
That was the only change from the weekend.
Vale made four changes to the side that lost 2-1 at home to Cheltenham on Saturday, a result that extended their poor recent run to five defeats and a draw in their last six League One outings.
The sides emerged into gathering mist on a cool, damp evening.
From kick off Clarke won a header for Stags but landed heavily on his back and needed a moment to recover.
Stags tore upfield and Swan got to the right by-line but overhit his cross.
Vale responded with some pressure of their own and three early corners.
On 10 minutes Pym was comfortably behind a low 20 yard shot from Arblaster after a neat turn.
Two minutes later Maris won a tackle, beat two opponents to set up Keillor-Dunn on the break, but Debrah stepped in with a fine block.
That forced the first of two home corners as the fog became heavier by the minute.
But Vale were close again on 14 minutes as Sang crossed from the right and Ojo should have hit the target with his seven yard header but sent it over.
A poor touch by Ojo almost let in Keillor-Dunn, Ripley racing out his box to head clear.
On 19 minutes Macdonald gave the ball away on the edge of his own box, Pym getting him off the hook with a good parry on Sang's powerful near post attempt.
Vale were even closer on 22 minutes. Garrity found Sang to his right and his cross was turned first time against the left post by Sheffield United loanee Arblaster.
Devine had a curling shot headed away for another Vale corner as the visitors continued to edge the evening.
Garrity went on a menacing run after a loose header by Bowery, but his final shot was poor.
Stags finally tested Ripley on 31 minutes as Keillor-Dunn met Reed's cross from the right with a searing volley from six yards but it was too straight and Ripley was able to block.
Vale forced two more corners amid more pressure and powerhouse striker Ikpeazu fired over the near angle on 42 minutes as the home side struggled to gain or keep possession.
But the sides went in all square with all to play for and the menacing fog thankfully receding a little.
However, Vale were ahead within five minutes of the restart with a superb strike by Devine.
Picking up a loose Reed block midway in the Stags half he ran forwards and picked out the bottom right corner with a firm, low finish from 25 yards.
Desperate for a way back in, Stags made a triple change just before the hour mark as Clarke, Swan and Maris made way for Boateng, Oates – a welcome sight after his injury – and Gale.
On 61 minutes an Ikpeazu cross bounced off the the top of the bar, then Pym saved well from Plant for a corner from which Ikpeazu headed over.
Oates got in a shot on the turn from Flint's cross that struck Gale and bounced wide but with a bit more luck could have gone in.
Smith saw the night's first booking for his foul on Lewis on 66 minutes.
Gale put Oates away on 69 minutes but Ripley as able to block with his knees from close range.
A contentious offside decision provoked home anger and Flint was booked for dissent on 70 minutes.
Vale forced two more corners as they looked for the killer second goal and Arblaster produced another spectacular turn before seeing his shot cannon off a defender for a corner.
McLaughlin also returned from a long term injury to replace Macdonald for the last seven minutes.
Vale sub Thomas was booked for delaying the game when the ball ran out near him as he warmed up on 87 minutes.
Cargill replaced Reed and Flint was thrown up front as we reached eight added minutes.
STAGS: Pym, Bowery, Flint, Brunt, Macdonald (McLaughlin 83), Reed (Cargill 90), Lewis, Clarke (Boateng 58), Maris (Gale 58), Keillor-Dunn, Swan (Oates 58). SUBS NOT USED: Flinders, Williams, Johnson, Cooper.
PORT VALE: Ripley, Sang, Smith, Garrity, Devine, Ikpeazu (Loft 62), Ojo, Lowe, Arbaster, Plant, Debrah (90+1). SUBS NOT USED: Leutwiler, Massey, Conlon, Shorrock, Walters, Dipepa, Thomas.
REFEREE: Thomas Bramall.
ATTENDANCE: 7,432 (1,644 away).