With Besiktas enjoying plenty of passionate support in the Tüpraş Stadium, the match began at a furious pace, and the home side came close to opening their account on several occasions, especially when Hyeongyu Oh flicked on a corner for Salih Ozcan, who missed the open goal by inches.
The Danish visitors gradually seemed to settle better into their game, but were then reduced to ten men after 15 minutes when Friday Etim was sent off for stamping on Tiago Djaló in the middle of the pitch. Coach Mike Tullberg reacted straight away by replacing Valdemar Byskov with Denil Castillo to boost the Danish defensive options.
The red card obviously turned the momentum in Turkish favor, and as the Danes were pushed back into their own box, Besiktas took advantage after 26 minutes as Orkun Kökçu received the ball unmarked on the edge of the Danish box and curled it into the right-hand corner beyond the reach of Midtjylland keeper Elías Olafsson.
Just three minutes later, the home side came very close to doubling their advantage when Olafsson managed to divert a wonderful volley from Michael Murillo in the box onto the crossbar and followingly, Junior Olaitan failed to get a touch to a dangerous cross when he was unmarked at the back post.
In the second half, Besiktas kept Midtjylland pinned to their own half as Tullberg's side struggled to relieve themselves of the relentless Turkish pressure that created countless dangerous situations in front of Eliasson's goal.
However, against the run of play, the Danish visitors then squandered a golden opportunity to restore parity ten minutes from the end when Phillip Billing was put clean through on goal, but former Bayern Munich keeper Alexander Nubel parried the effort for a corner to preserve the Turkish lead. Still, the Danes prevented further damage which sets up an enticing encounter in a week's time.