It was clear that when the visitors upped the pace, the newly promoted home side struggled to keep up. Jakob Neestrup's side have now won their first three matches of the season in the Danish Superliga.
The match scenario was hardly surprising from the start as FC Copenhagen seized the initiative while Fredericia were content to defend deep.
Fredericia were well organised defensively, and apart from a few attempts, the visitors failed to create any clear-cut scoring opportunities.
Therefore, a set piece was needed after 35 minutes for the visitors to break the deadlock.
A free kick from Marcos Lopez was headed across the goal by Thomas Delaney to an onrushing Elias Achouri, who put the visitors in front.
Fredericia wasn't capable of threatening the visitor's rearguard, but they did have a couple of attempts at the end of the first half.
Twice, the newly purchased goalkeeper, Dominik Kotarski, was caught in no man's land, causing panic in the Copenhagen defense, especially on the second occasion, but the attempt from Patrick Egelund sailed wide of the target.
It was clear that the visitors are in the midst of a tight match schedule with important European qualifiers, because they didn't put much effort into the second half.
However, 20 minutes before the end, the visitors upped the pace again when Jordan Larsson combined with Magnus Mattson on the left side, before the Swedish striker curled a beautiful effort into the far left-hand corner of the goal.
Fredericia wasted a few half-chances in the final phase, but they never really threatened to cut the deficit.
Neestrup's side can now focus on Tuesday, when the first of two important matches against Malmö FF awaits in the Champions League qualifiers.
In the other Superliga match of the day, Vejle recorded their first win of the season, when they thrashed OB at home 4-0.
OB otherwise went into the match high on confidence after a bright start to the season, with four points after the first two matches.
Vejle's three summer signings, Ghanaian youth international ghanesiske Bismark Edjeodji, Andrew Hjulsager, and Mikkel Duelund, really put on the show and ran the visitors ragged in a match where Vejle showed that they can turn into a force to be reckoned with after they were nearly relegated last season.