Oldham are one game away from Wembley after outclassing Bradford to win 2-0 in the Johnstone`s Paint Trophy northern area semi-finals.
Kuqi blazed over an early chance before Latics goalkeeper Alex Cisak was forced to save well from James Hanson. Josh Parker went close for Paul Dickov`s side and two openings were wasted before the break as Luca Scapuzzi volleyed off target and then shot straight at Jon McLaughlin.
The breakthrough came in the 61st minute when Scapuzzi cut in from the left and Adeyemi took over on the edge of the box, skipping past two challenges and slotting home from 10 yards.
Bradford substitute Ross Hannah tested Cisak, but only fine goalkeeping from McLaughlin denied Kuqi at point-blank range. There was no stopping Kuqi 10 minutes from time, though, as he sealed the Bantams` fate with an unstoppable six-yard header from Robbie Simpson`s right-wing free-kick.
Bradford Craig Fagan slammed a 90th-minute penalty atrociously high and wide after defender Jean Yves Mvoto was punished for handball.