The Danish Superliga side took control from the outset as Marc dal Hende found the net in the fourth minute.
Kristian Riis sidefooted in and captain Jakob Poulsen scored from the penalty spot to make it 3-0 at half-time.
Simon Kroon was on target twice in two minutes around the hour mark, before Ronan Curtis pulled one back, but Bozhidar Kraev added his side's sixth.
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The League of Ireland Premier Division side went into the game as underdogs against a Danish outfit who recently finished fourth in their league and qualified for Europe through a play-off.
The home side were two goals to the good within a quarter of an hour, then Derry had their first chance but striker Rory Patterson shot wide.
Gerard Doherty saved one-on-one with Paul Onuachu but Poulsen increased his side's lead prior to the interval.
Derry had a penalty appeal turned down early in the second half when Ronan Curtis appeared to be brought down inside the area, but Kroon's double salvo somewhat sapped the morale of Kenny Shiels' side.
Curtis's consolation was followed by Kraev's goal to leave next week's second leg at the Sligo Showgrounds seemingly a formality.
The winners will face Ferencvaros of Hungary or Jelgava of Latvia in the next qualifying round of the competition.
Derry City were thumped 6-1 by FC Midtjylland in the first leg of their first round Europa League qualifier.