Mexican winger Roberto Huescas was last week charged with reckless driving and could face prison but was still selected for tonights starting line-up by coach Jacob Neestrup.
That turned out to be a good idea as he provided the set-up for the opening goal after 20 minutes when he delivered a pin-point-pass for Magnus Mattsson to give the home side the lead with a bullet header.
The goal was thoroughly deserved after FC Copenhagen totally dominated the greater stages of the first half and they were only desperately unlucky not to head into the interval with a 2-0 lead, when Victor Froholdt, who was recently given his debut in the Danish national team, hit the woodwork with a stinging drive.
The home side continued to dominate proceedings in the second half and Randers were only able to threaten the FC Copenhagen goal on very rare occasions and had their best attempt to find the net after an hour's play, when Mohammed Toure rose high to meet a cross but the ball fizzled wide of the post.
The home side had chances to build on their lead in the second half but as they failed to convert, the biggest cheer of the night arrived when Lukas Lerager, Roony Bardghji and Andreas Cornelius all coming back from injury were introduced towards the end of the match.
Thanks to the win Jacob Neestrup's men narrowed the gap to FC Midtjylland to one point with nine matches left to play in the Superliga.