Darko Lazovic scored a superb 63rd minute opener for Red Star and his Colombian striker Cristian Borja put the icing on the cake when he shook off a challenge from a defender and powered his shot past goalkeeper Vladimir Stojkovic.
The 1991 European Cup winners were joined by unfancied Borac Cacak, who reached their first final in any competition after a 1-0 win at Vojvodina Novi Sad sent them through following a goalless first leg.
Partizan dominated long spells in both legs of the tie and created a hatful of gilt-edged chances but poor finishing cost them dearly as Red Star fans celebrated by lighting dozens of flares in the second half.
The home team's coach Avram Grant, who steered Chelsea to the 2008 Champions League final, fielded an adventurous 4-3-3 formation but could only watch in anguish as his players squandered one opportunity after another.
A dejected-looking Grant told a news conference: "Like in the first leg we missed too many chances and had to take risks in the second half which made it difficult to stay focused and they took full advantage."
Goalkeeper Stojkovic was powerless when his Partizan team-mates failed to clear a corner and Lazovic pounced to effectively seal Red Star's success and delight the visiting end of the 30,000 crowd.
They were on song again as Borja muscled through Partizan's defence in the closing stages and made sure Red Star also celebrated their first away win over Partizan since 2007.
"It was tactically a very mature performance from my team, who deserved to win this excellent game of football played in a cracking atmosphere," said Red Star coach Robert Prosinecki.
Borac, battling to avoid relegation from the first division, secured an unlikely win at Vojvodina whose Karadjordje stadium will host next month's final for the first time.
Vojvodina, twice national champions in the former Yugoslavia and losers in five cup finals, were stunned when Filip Knezevic drilled an unstoppable shot into the roof of the net after a dazzling solo run by substitute Ivan Jovanovic.
"This is definitely the best game of football we have played all season and I can only congratulate my team for playing their hearts out to defy the odds and reach the final," said Borac coach Slavko Vojicic.
