This victory was as smooth and serene as Manchester City’s passage into the draw for the quarter-finals on Friday week. Going into this second leg 3-1 up, Pep Guardiola sent out an XI that rested the frontline artillery of Kevin De Bruyne, Phil Foden, John Stones, Bernardo Silva, Nathan Aké and Kyle Walker before the crunch match against Liverpool at the ­weekend – and ­Copenhagen still trailed 3-1 at the break, 6-2 on aggregate.

Manuel Akanji, Julián Álvarez and Erling Haaland were City’s scorers, Mohamed Elyounoussi registering Copenhagen’s consolation as the ­second half became an exercise in keeping shape and concentration for Guardiola’s side.

Related: Manchester City v FC Copenhagen: Champions League last 16, second leg – live

Whichever team City are paired with in Nyon will provoke zero fear in the ranks or with Guardiola, whose supreme unit remain headed for what would be a quite remarkable defence of the treble.

“We are a team that believes we can do it,” Guardiola said. “Listen, we’re competing with Real Madrid and Bayern Munich. We don’t know who we are going to face. It’s a question of wait and see. The important thing is seven years in a row we are there [in the quarter-finals]. If you play against Bayern Munich [for example] – how many Champions Leagues they have [six] and their history . We are scared too but at the same time we are like in a dream to be here.

“I said to the players: ‘For me, every time we go through, wow, I know how difficult it is.’ Today Madrid suffered to go through [2-1] against Leipzig. The people take it for granted. That is good, our standards are there but we know internally it is difficult but everything is so complicated.”

What Copenhagen did not need was to concede twice, inside five ­minutes. Diligent work from Rico Lewis ensured a corner and from here it was simple for the holders. ­Álvarez swung the ball into the area, Peter Ankersen failed to handle Akanji and he volleyed beyond Kamil Grabara.

City’s second soon followed. This time Álvarez scored – from his own corner, on the left. The No 19’s ­delivery was headed against the bar by Rodri, the ball bounced back to him, and Álvarez unloaded straight at Grabara: the masked No 1 flapped at the shot and pushed it in.

At 5-1 up overall in the tie an obliteration was on. Mateo Kovacic ­requiring treatment allowed Jacob Neestrup to have a chat with his p­layers. The message had to be to keep it tight for as long as possible and see where it took them.

No advice, though, can mitigate when being a class or two below as Neestrup had also conceded. Oscar Bobb was an apt emblem of this. Fielded in only a second competition start as the No 10, the 20‑year‑old floated about, receiving the ball, ­making piercing darts and offloading.

Bobb, though, was culpable when Copenhagen scored. A loose pass from the Norwegian allowed the Danish club to break. Elyounoussi skipped down the left, cut infield and tapped to Orri Óskarsson. A slick backheel returned the ball and the No 10 struck.

Guardiola took the arm of Rohit Saggi as he argued a point with the fourth official in a sign of frustration that was eased when City scored in the period’s added time. Rodri dropped a diagonal into Haaland who lurked in an inside-right zone in the area: he controlled, shimmied between Scott McKenna and Elias Jelert and beat Grabara to the ­latter’s left.

Guardiola’s move for the second half was to give Rodri a rest before the trip to Anfield on Sunday in a rejig that had his replacement, ­Sergio Gómez, go to the left, Álvarez move across and Kovacic drop into the Spaniard’s pivot role.

The atmosphere was becalmed but what Guardiola desired was ­seeing his charges keep to the ­patterns and rhythms in which he drills them. The carousel passing of Josko ­Gvardiol, Kovacic, Rúben Dias, Bobb, Álvarez et al will have pleased then and, as the contest moved beyond the hour, the temptation to bring off Haaland grew.

Related: Vinícius edges Real Madrid past tenacious RB Leipzig and into last eight

In his first City campaign Matheus Nunes has convinced more and more. Stationed on the right, the Portuguese’s fluid ­movement inside throughout ­displayed a ­comprehension of ­Guardiola’s ­geometric demands, as did a jink along his flank, pirouette, and simple lay-off to a colleague in a ­better area.

Now, Ederson showed he is versed in the goalkeeper’s need to always be alert when stopping a Magnus ­Mattsson snap-shot at point‑blank range, and when Guardiola made a second substitution it was to hand Stones a 22‑minute run out, Dias given the breather.

Nunes was taken off with what appeared to be a painful finger problem. In the away end Copenhagen’s faithful danced and sang. Their spirit deserves credit, as do City for the relentless quality.

Neestrup offered a pithy verdict on City. “They work fucking hard,” the Copenhagen manager said.