The Jutland underdogs helped create an entertaining match but truth to be told, the difference in level was to much to overcome for Sancheev Manoharan's outfit.
The match saw 13,205 spectators pass through the gates at the Blue Water Arena, where the Esbjerg faithful are very hungry for top football after five years outside best Danish domestic league.
But despite the pressure from the stands, FC Copenhagen took full control of the match from the start, scored two goals in the first 15 minutes and were generally in full control.
The Esbjerg players had hardly touched the ball before Viktor Dadason, after six minutes of play, poked the ball into the net at the back post after a fine delivery across the face of goal from Youssoufa Moukoko.
Eight minutes later Moukoko turned provider again, this time laying the ball into the path of Mohamed Elyounoussi who searched past Andreas Troelsen and scored with a flat finish past goalkeeper Robby McCrorie.
After 35 minutes, the visitors made it 3-0 when McCrorie was caught out of his comfort zone, and Dadason sent the ball across goal for the onrushing Elias Achouri, who scored from close range.
The home side then got a lifeline shortly before the break when Muamer Brajanac reduced the deficit by lobbing the ball over Dominik Kotarski.
In the second half Dadason made his second goal of the night 18 minutes before the end to make it 4-1 before Peter Bjur straight after elegantly curled the ball beyond the reach of Kotarski to make it 4-2.