The La Liga giants held a 4-1 advantage heading into Thursday night's second leg in Spain, and Kevin Gameiro's early strike proved enough to give his side a comfortable night at the Wanda Metropolitano.
Diego Simeone opted to name a strong starting lineup - despite Copenhagen needing at least four goals to remain in the tie - but the Atletico boss got what he was looking for as the home side took the lead within seven minutes of kickoff.
The ball was worked to Gameiro on the edge of the penalty area and the forward wasted no time in lashing a well-struck effort into the bottom corner from 25 yards out.
Moments later, it was almost 2-0 as Fernando Torres saw a close-range effort well blocked by a defender but as the first half progressed, Copenhagen managed to find their feet and nullify the threat being offered by their hosts.
After the half-hour mark had passed by, Torres was provided with the chance to head on goal from 14 yards, but the Spaniard's effort lacked direction and went wide of the far post.
Such was Atletico's dominance that Copenhagen boss Stale Solbakken opted to take off two of his key men - William Kvist and Viktor Fischer - at the break, and it was an acknowledgement that the tie was already over as a contest.
Copenhagen were not prepared to sit back with Andrija Pavlovic drilling a shot just wide of the post from distance, but Atletico should have wrapped up the win on the night on 64 minutes through Gameiro, only for Stephan Andersen to come out quickly and block the forward's shot.
During the closing stages, substitute Nicolas Gaitan drilled a shot just wide of the far top corner, but Copenhagen almost netted a dramatic equaliser through debutant Jonas Wind, only for the youngster to fire too close to Oblak from inside of the penalty area.
Copenhagen continued to push for what would have been a deserved equaliser on the night, but Atletico held firm to register their six successive victory in all competitions.
ATLETICO MADRID (4-4-2): Oblak; Juanfran, Gimenez, Godin, Sergi; Koke (Saul 46'), Gabi, Correa (Gaitan 60'), Vitolo; Gameiro (Partey 68'), Torres
COPENHAGEN (4-4-2) : Andersen; Ankersen, Vavro, Luftner, Bengtsson; Thomsen, Gregus, Kvist (Skov 46'), Fischer (Falk 46'); Sotiriou (Wind 80'), Pavlovic