Randers are still rock bottom of the fledgling SAS-Ligaen table after suffering their fourth loss of the season, 3-1 at home to Brondby.
Michael Krohn-Delhi put the visitors ahead four minutes from the break before Soren Berg levelled matters in the 74th minute. But half-time substitute Peter Madsen restored Brondby's lead a minute later and the result was sealed by Allan Jepsen's own goal two minutes from time.
Randers, who finished fifth last season, only have one point from five games.
Elsewhere, Koge picked up their second point of the season after they secured a late 1-1 draw against high-flying Nordsjaelland. Rawez Lawan's 63rd-minute goal looked to have sealed it for the visitors, but Fabinho pounced four minutes from time to snatch a share of the spoils for Koge.
Nordsjaelland are now third, five points behind leaders AGF Aarhus with a game in hand.
In other action, Esbjerg ran out 3-2 winners at Silkeborg. The visitors were in control from the start and took the lead in the first minute through Tim Janssen before Soren Rieks doubled their advantage in the 14th minute.
Rajko Lekic pulled one back in the 58th minute, but Jesper Lange restored Esbjerg's two-goal cushion seconds later. Substitute Kaimar Saag, who had been on the pitch nine minutes, nabbed a late consolation for Silkeborg right at the end.
