The Jutland visitors began brightly in Copenhagen and thought they had taken the lead after seven minutes when Jeppe Gronning slotted the ball into the net beyond the reach of Dominik Kotarski from close range, but Gronning was adjudged to be in an offside position.
Instead, the home side grabbed the opening goal after 14 minutes when William Clem intercepted a careless pass from Viborg goalkeeper Lucas Lund, rounded the keeper, and coolly made it 1-0 to spark off celebrations in the Parken Stadium.
Viborg, however, never gave up and were rewarded for their tenacity eleven minutes later, when Charly Nouck searched down the right flank and provided a pinpoint delivery for the onrushing Dorian Junior, who kicked the ball into the roof of the net from close range to restore parity.
Coach Jacob Neestrup must have spoken harsh words during the interval, as FC Copenhagen began the second half much more determined, which allowed them to restore their lead four minutes after the restart when Mohamed Elyounoussi rose high to head home a delivery from Oliver Hojer as goalkeeper Lucas Lund failed to clear the inswinging cross.
Towards the end, Viborg put the home side under intense pressure and came close to making it 2-2 when Kotarski had to react quickly to keep out a header from Tim Freriks, but FC Copenhagen hung on for the narrow win.