The 4-4 aggregate result, coming after last week's first leg in Barcelona finished 3-2, prompted wild celebrations at the club's 6,000-capacity stadium in Miranda de Ebro and set up a semi-final against Athletic Bilbao or Real Mallorca.
It was only the second time a team from the third level of Spanish football has reached the last four of the cup, as Mirandes, who have an annual budget of just over 1.2 million euros, followed up their unlikely successes against La Liga clubs Villareal and Racing Santander with another heroic display.
"This is amazing," captain Pablo Infante, a local bank employee who netted the equaliser and provided the assist for the dramatic winner, told Spanish television.
"Tomorrow I have to go to work but we are going to celebrate a bit first," he added.
"Incredible. I am speechless. Spectacular, that's what football is all about," Fabregas wrote on his Twitter feed.
Bilbao are Mirandes's likely opponents in the last four after they beat La Liga rivals Real Mallorca 2-0 at the San Mames last week, with the return leg in Palma on Wednesday.
The build-up to the game has been overshadowed by the controversy surrounding Pepe's alleged stamp on the hand of Barca's World Player of the Year Lionel Messi during the first leg in Madrid.
