Dragan Bogavac addesd the third for OFK, who completed a rare double over Red Star after beating the 1991 European Cup winners 1-0 at home in a league fixture earlier this month.
OFK were joined in the semis by Jagodina, 1-0 winners at Rad Belgrade, as well as Javor Ivanjica and Vojvodina Novi Sad who beat their respective rivals in penalty shootouts.
Brimming with confidence after Saturday's 3-2 league win over bitter foes Partizan Belgrade, Red Star were quickly brought down to earth when keeper Aleksandar Kirovski's poor clearance ricocheted off the unsuspecting Grbic into the back of the net.
Serbia forward Darko Lazovic equalised with a scorcher from 20 metres after both sides had missed sitters in a lively first half, but OFK showed no nerves and played their more illustrious rivals off the park after the interval.
Grbic, who also scored OFK's winner in the league fixture, was on target again on the hour mark when he nodded the ball past the stranded Kirovski, who was unable to recover after parrying two close-range efforts.
Bogavac sealed the match barely a minute later when the home side lost possession and the former Red Star striker exchanged a one-two with Marko Petkovic before dispatching a delicate lob over the advancing Kirovski.
Milos Lepovic scored a 61st-minute winner to send Jagodina into the last four for the first time, while Javor Ivanjica followed suit by beating Borac Cacak away 5-4 on penalties after a goalless draw at fulltime.
Vojvodina were flirting with elimination after falling behind to a Darko Puskaric goal at Spartak Subotica but Aboubakar Oumarou equalised in the 89th minute and the visitors went on to win the penalty shootout 5-4.
The semi-finals will be played after the December-March winter break.
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- Javor Ivanjica