The champions, who face Chelsea in London in the second leg of their Champions League round of 16, retain their massive 19-point lead at the top of the table, but manager Stale Solbakken was far from happy.
"Everyone can have a bad day, but it didn't work technically or tactically," he told reporters after the game.
FC Midtjylland who move into second place ahead of Odense BK, who play Monday.
At the bottom of the table, just eight points separate seven of the league's 12 teams. Bottom club Aalborg looked on course for a much-needed victory only for Silkeborg to grab a share of the points courtesy of an 87th minute penalty from Rajko Lekic.
A 4-0 defeat to Randers rounded off a bad week for FC Nordsjaelland, whose coach Morten Wieghorst announced on Wednesday that he will leave at the end of the season to take over the Danish Under 21 side.
Norsjaelland are now third from bottom on 22 points, five ahead of Esbjerg and Aalborg.
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