Record winners Real Madrid laboured to a 1-1 draw against fighting RB Leipzig for a narrow escape into the Champions League quarter-finals alongside title holders Manchester United who cruised to a second 3-1 win over Copenhagen on Wednesday.
Real won the last 16 first leg tie 1-0 last month in Germany but registered no shot on target in the first half at the Bernabeu.
Vinicius Junior eventually put them 1-0 up in the 65th but Leipzig captain Willi Orban levelled three minutes later. Real had to sweat it out until the end to prevail 2-1 from both legs, with Dani Olmo chipping onto the top of the Real crossbar in stoppage time.
"We can live with the result but not with the way we played," Real midfielder Toni Kroos told streaming portal DAZN.
"Leipzig did a good job, they defended well and were good on the counter. We didn't create enough danger and must learn from that."
City meanwhile advanced 6-2 on aggregate from goals by Manuel Akanji in the fifth, Julian Alvarez four minutes later and Erling Haaland in first-half stoppage time on the night. Mohamed Elyounoussi scored for the Danish visitors.
It was City's 10th victory in a row in the elite event as they reached the last eight for a seventh straight season.
"The first two goals in first half made it easier for us. We tried to do our best and did what we had to do," Akanji told TNT Sport.
Looking ahead, he added: "We will see how the tournament goes. We feel good right now. We're confident going into the next round. We are one of the favourites but have to prove it."
Real and City join Bayern Munich and Paris Saint-Germain, who qualified Tuesday, in the last eight.
The remaining four last 16 return legs are next week, followed by the March 15 quarter- and semi-final draw en route to the June 1 final at Wembley.
In Madrid, Leipzig faced a daunting task after their unlucky home defeat but attacked with courage against a Real side including Jude Bellingham who was red carded last weekend in La Liga and banned for two top flight games.
Benjamin Sesko was denied by goalkeeper Andrij Lunin and Lois Openda aimed wide right in the 15th.
Shortly before the break Lunin had to save again from Simons, and Openda smashed inches left as Real fans jeered their passive team.
Second-half substitute Rodrygo hit the side netting in the 63rd as the hosts finally threatened, and they were 1-0 up two minutes later when Bellingham set up Vinicius Junior to fire into the left corner.
But Leipzig failed to bow and levelled three minutes later when Orban nodded home David Raum's cross.
The visitors pressed for a second to reach extra time as Orban headed wide in the 82nd and Olmo, a Barcelona academy product, then lobbed the ball onto the top of the bar but Real eventually escaped.
"Looking at the 180 minutes we had better chances than Real. I don't know how they scored again today," Leipzig's Benjamin Henrichs said.
"We should not have been eliminated, given the amount of scoring opportunities we had."
City manager Pep Guardiola made seven changes to the side that beat Manchester United last weekend, seemingly already looking ahead at Sunday's big Premier League trip to leaders Liverpool.
Only goalkeeper Ederson, Ruben Dias, Rodri and Haaland remained in the starting 11 but it didn't matter as the holders ended any possible doubts in the opening nine minutes at the Etihad.
Akanji first volleyed Julian Alvarez' corner kick home, and Alvarez' speculative effort was fumbled into the net by Copenhagen goalkeeper Kamil Grabara after Rodri had headed against the crossbar.
Copenhagen did however not throw in the towel, became a little more adventurous, and got on the scoreboard on the counter in the 29th from Elyounoussi's low shot after a one-two with Orri Oskarsson.
But Haaland then made it 3-1 in the third minute of stoppage time for his 41st Champions League goal, drawing level with former City great Sergio Aguero, and the goal also marking the final score.
