Due to travel restrictions caused by the Covid-19 pandemic, City and their German opponents Monchengladbach met at Puskas Arena in Budapest as they did in the first-leg, Xinhua news agency reported.
Bringing a 2-0 lead to the second meeting, City started brightly with two goals in the early stages.
City captain Kevin De Bruyne opened the scoring by lashing home Riyad Mahrez's pass 12 minutes into the first half. Six minutes later, Phil Foden assisted German international Ilkay Gundogan to add a second with a close-range low shot.
Monchengladbach failed to respond, meaning the English Premier League leaders advance 4-0 on aggregate.
In Madrid, the hosts broke the deadlock in the 34th minute with Karim Benzema sweeping home after Atalanta goalkeeper Marco Sportiello's poor clearance giving Luka Modric the opportunity to feed the French international.
In the second half, Sergio Ramos put Real Madrid further ahead from the penalty spot before the Italian side pulled one back with Luis Muriel's free-kick. Marco Asensio then sealed the 3-1 win for the hosts with an 84th-minute goal.
Madrid advances 4-1 on aggregate. The 13-time champions reached the quarterfinals for the first time in three seasons.
The quarterfinal draw will take place on Friday.
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