Michael Carrick witnessed his side's seven-match winning streak come to an end on Saturday as Boro suffered a 2-0 defeat at home to Stoke City.
The Championship outfit appeared up against it when their League One opponents took an early lead through Ryan Trevitt's opener in the 13th minute.
However, despite going into half time trailing, Boro were ahead by the hour mark, Morgan Rogers's curling effort getting them back on level terms before Samuel Silvera put the visitors ahead just before the hour mark.
In an eventful appearance, Trevitt scored a second to bring Exeter level in the 66th minute, only for his foul in the penalty area giving Emmanuel Latte Lath the opportunity to score the winner from the spot eight minutes from time.
While Middlesbrough were last in the quarter-finals of this competition just five years ago, Port Vale have reached the last eight for the first time in their history.
Although the Staffordshire outfit were facing a team in Mansfield Town who play in a division lower, their hosts had not suffered a single defeat all season.
That has now changed with Alfie Devine's long-range strike shortly after the interval proving to be the difference at Field Mill.
These two teams will now wait to see who progresses from the six other ties on Wednesday night ahead of the quarter-finals being played the week before Christmas.