Peter Bosz's men had been expected to outclass the Cypriot minnows but they are now in danger of suffering a group-stage exit as they have yet to secure victory in the group where Real Madrid and Tottenham Hotspur lead the standings with seven points apiece.
The lacklustre game sparked into life just after the hour mark when Apoel took the lead through substitute Mickael Pote following a goalkeeping error.
A strike from Sokratis Papastathopoulos allowed Dortmund to draw level five minutes later but they were unable to score again.
Along with Apoel, they have one point in Group H.
Apoel opened the score in the 61st minute when Pote took advantage of a defensive lapse, rounding Roman Burki in the Dortmund goal after the keeper could only parry Lorenzo Ebecilio’s effort from the right hand side of the area.
Dortmund drew level when Mario Gotze’s floated cross to the back post was headed in by Papastathopoulos after the Greek defender stayed up following a corner.
This appeared to wake the Germans from their slumber and just a minute later, Shinji Kagawa’s strike from the edge of the box was tipped onto the bar by substitute keeper Raul Gudino.
Dortmund almost snatched it at the death but Pierre-Emerick Aubameyang’s header was shovelled onto the post by Gudino before Gotze blazed the rebound over with the last kick of the game.
(Reporting by Peter Stevenson, editing by Pritha Sarkar)
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