Red Star registered their first win in 10 games over Partizan after an Andrija Kaludjerovic goal gave them a 1-0 second-leg win at home, but ultimately paid the price for poor finishing in both games.
Partizan will be chasing their 12th Cup triumph in the final on May 11 and Vojvodina Novi Sad their first after a 1-0 home win over Sloboda Point Sevojno gave them a 3-1 overall victory in the other semi-final.
Having taken a two-goal cushion from the first leg, Partizan sat back in a defensive formation and were thoroughly outplayed by Red Star who will rue missing a hatful of good chances.
Partizan keeper Vladimir Stojkovic denied Kaludjerovic with a reflex save early on, while Colombian midfielder Cristian Borja and striker Aleksandar Jevtic headed chances wide before the hosts eventually broke the deadlock.
Kaludjerovic poked the ball past Stojkovic in the 72nd minute after good work by Borja and 10 minutes later he wasted a golden chance to send the tie into a penalty shootout, firing over the bar from 12 metres after beating his marker.
Partizan could have snatched what would have been a hardly deserved equaliser in the 88th minute when left back Aleksandar Lazevski saw his shot superbly palmed away by Red Star keeper Boban Bajkovic.
"The means justifies the end and although we didn't shine, it's a great feeling to knock your biggest rival out of the competition to advance to the final," Partizan coach Aleksandar Stanojevic told Serbian television.
"We had to hang on and it could have easily gone to penalties but we knew it wasn't going to be a walk in the park even though we had a 2-0 advantage from the reverse fixture."
Belgrade's big two will meet again on April 23 in a league match, with leaders Partizan three points ahead of Red Star and their sights set on winning a record fourth successive title.
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