Celtic was unable to win a 10th successive Scottish Premiership title last season as Rangers ended its long drought, meaning Celtic has had to start in the second round of Champions League qualifying.
And Midtjylland – runner up in Denmark last term – proved stubborn opposition, looking particularly bright in the early stages.
Though Celtic opened the scoring in the 39th minute, Israeli youngster Liel Abada – a new signing from Maccabi Petah Tikva – turning in from the middle of the box after Jonas Lossl could only parry an initial effort from Ryan Christie, who had hit the post not long prior.
Nir Bitton then put Celtic's position in doubt, reacting angrily to an apparent dive by Anders Dreyer and earning a second booking for poking the winger in the face.
But Dreyer – who was also yellow-carded in that prior incident – did not last much longer either, with referee Sandro Scharer making the arguably harsh decision to dismiss him in the 56th minute for what he perceived to be another display of simulation.
Celtic might have fancied its chances to finish the job after that, and it did swiftly hit the crossbar through Callum McGregor.
But unconvincing goalkeeping from Vasilios Barkas 10 minutes later allowed Evander to send a free-kick into the top-right corner, and that sealed a draw.
The two teams meet again in Denmark next Thursday (AEST), though Celtic's saving grace is away goals no longer count double as a tie-breaker.