The result lifted Red Star, serving a crowd ban for fan violence in their city derby against champions Partizan this month, into pole position with 26 points from 13 games.
Partizan, who were also handed a crowd ban for their share of the derby trouble when fans lit a huge bonfire, are two points behind Red Star heading into their game in hand at neighbours Vozdovac on Sunday.
Thiago Galvao fired Sloboda into an early lead with a spectacular overhead kick but their joy was short-lived as Goran Logic levelled with a towering header from a corner.
Former international striker Mrdja opened his account in the 40th minute with a calm finish from 10 metres and volleyed his second shortly before halftime.
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Red Star sealed their win on the hour after Mrdja completed his second hat-trick of the season, sweeping in a close-range rebound after Sloboda keeper Dean Rankovic parried Neck Pecnik's effort.
(Writing by Zoran Milosavljevic; Editing by Ed Osmond)
