Partizan, aiming for a record sixth successive championship, were 2-0 winners at home to city rivals OFK thanks to second-half goals from striker Aleksandar Mitrovic and midfielder Predrag Luka, who joined the club during the mid-season break.
Red Star's defeat is likely to pile more pressure on coach Aleksandar Jankovic, who barely kept his job after the 1991 European champions produced below-par performances in the first two games after the season resumed at the end of February.
Last weekend's 3-0 home win against struggling Novi Pazar turned out to be a flash in the pan as Red Star were thoroughly outplayed by Radnicki and were fortunate not to have lost by a bigger margin after defender Nikola Petkovic was sent off for two bookable offences.
"The coach is always the most responsible person for a slump and I will certainly have words with the staff in the coming days, but this is neither the time nor place to talk about it," Jankovic told reporters.
"We were second-best in every department today and Radnicki completely deserved their victory," he said.
Marko Ljubinkovic headed Radnicki into a first-half lead after twisting in mid air to meet Aleksandar Jovanovic's cross from the left and Petar Skuletic made it 2-0 when he rounded off a flowing move with a crisp shot that cannoned in off the crossbar.
Striker Filip Kasalica pulled one back for Red Star with a diving header in the closing stages but the home side held out comfortably to delight their vociferous fans.
Owing in excess of 50 million euros to various creditors and unable to pay players' wages regularly, once mighty Red Star are facing a trophyless season. They have been knocked out of the cup and were eliminated in the Europa League preliminary rounds last September.
Partizan took full advantage of their neighbours' mounting woes after Mitrovic weaved his way into the penalty box and smashed an unstoppable shot from 10 metres into the roof of the net before Luka sealed the win with a neat far-post header.
"OFK defended well in the first half and threatened on the break so we had to move up a gear after the interval to chalk up three very important points," Partizan coach Vladimir Vermezovic told Serbia's Arenasport television.
"There will be no resting on laurels though and we have to keep up the momentum to stay in the driving seat." ($1 = 0.7654 euros)