OFK Belgrade also reached the last four with a 2-0 win at Sloboda Uzice. Holders Jagodina are at home to Donji Srem and former European champions Red Star Belgrade entertain Vojvodina Novi Sad in the evening kickoffs.
Dino Sarac volleyed Spartak into an 11th-minute lead and set up a close-range second for Aleksandar Noskovic against league champions Partizan who had goalkeeper Vladimir Stojkovic to thank for keeping down the margin of defeat.
"It's difficult to beat a side of Spartak's quality twice in only a few days but we were very poor today and having fallen two goals behind so early there was no way back," Partizan coach Vuk Rasovic told Arenasport television.
Spartak are eighth in the league, 10 points behind leaders Partizan.