Jonas Wind levelled the tie with his first goal in the fourth minute and put his side ahead from the penalty spot in the 53rd minute.
Rasmus Falk added the third in the 62nd minute to seal their place in the last eight and a potential tie against United, who held a 5-0 advantage going into the second leg of their last-16 tie.
More to follow
Striker Jonas Wind celebrates after scoring a goal for Copenhagen on Wednesday night
Istanbul Basaksehir defender Martin Skrtel tackles Copenhagen’s Mikkel Kaufmann