After a messy start to the game, FCK opened the score midway through the first half, although the goal was initially not awarded.
However, a VAR check determined that the ball was clearly over the goal line, as Randers defender Oliver Olsen was unlucky to push it into his own net after FCK captain Thomas Delaney had headed a corner across the box to hit the unfortunate Olsen.
Five minutes later, FCK striker Jordan Larsson doubled the lead after a classy delivery from winger Robert, who showed plenty of skill, taking the ball past Olsen.
Randers showed no virtually no attacking initiative before the break but that scenario was to change completely after the interval where it only took them seconds to cut the deficit when Florian Danho delivered a nice through-ball for attacking partner Simen Nordli who scored with a clinical low drive.
Danho and Mathias Greve subsequently had chances to restore paity but FC Copenhagen hung on to claim their first three points after the restart.
FC Copenhagen are thus back at the top of the league where they are level on points with FC Midtjylland. The two top teams, who both won this weekend without showing their best football, have 36 points after 18 games in the regular season.
AGF is third with five points less, while Brøndby and Randers are a further point behind.