Goals from Guinean import Naby Laye Keita and Kwame Boahene gave the Porcupines a ticket to the next round, with Ebenezer Aboagye scoring the lower division side's only goal at Kumasi's Baba Yara Sports Stadium.
Shafiu Mumuni emerged the hero for the Miners as he connected to a Godfred Asiamah cross to score the decisive goal in the 54th minute.
Elsewhere, Division One side Unistar Academy, who shockingly eliminated Premier League giants Hearts of Oak in the Round of 16, continue their good run with a 3-1 win over fellow lower-tier outfit Proud United, who accounted for top-flight side Liberty Professionals in the previous round.
In the last game, Nzema Kotoko beat Heart of Lions 4-1 on penalties in an all-lower division fixture to set up a date with Unistar.
The semi-final fixtures are scheduled for June 19 and 20 and the ultimate winners of the competition will represent Ghana in next season's Caf Confederation Cup.