Raphael Guerreiro put them ahead in the 29th and the Germans, 2013 finalists, should have scored several more in the first half before APOEL's Mickael Pote stunned the home crowd with a superb equaliser six minutes after the restart.
The result did neither team a favour with both on two points from four matches, five behind second-placed Real Madrid, who lost to group leaders Tottenham Hotspur.
Dortmund, who host Tottenham on Nov. 21 before travelling to Madrid for their final group game, had four shots on goal after only 10 minutes.
Desperate for their first win in the group that would keep their slim qualification hopes alive, they were in complete control from the start.
APOEL kept plenty of bodies behind the ball and looked to have tamed Dortmund until a defence-splitting pass from Shinji Kagawa on the half hour sent Guerreiro through for the first goal.
Dortmund, who face Bayern Munich in the Bundesliga on Saturday, squandered a bagful of chances through Japan international Kagawa and Pierre-Emerick Aubameyang.
They were punished for their wastefulness when Pote turned beautifully in the box and fired in the equaliser in the 51st minute, his second goal against Dortmund after also scoring in their draw in Cyprus.
Despite having more than 70 percent possession and hitting the bar with Aubameyang late in the game the hosts could not find the winner.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
