After claiming a 3-1 first-leg win in Denmark three weeks ago, victory by the same scoreline in the reverse fixture on home soil ensured the Citizens secured safe passage through to the quarter-finals for a seventh successive season - the longest current run of any team in Europe.
Pep Guardiola's side raced into a two-goal lead inside the opening 10 minutes thanks to a well-struck volley from Manuel Akanji following a corner, and a long-range strike from Julian Alvarez that slipped through the gloves of Copenhagen goalkeeper Kamil Grabara.
The visitors pulled one back just before the half-hour mark, with former Southampton man Mohamed Elyounoussi rounding off a swift counter-attack to slot home the Danish club's first-ever Champions League goal in England.
However, City restored their two-goal cushion on the night when Erling Haaland clinically swept a left-footed shot into the bottom-right corner in first-half stoppage time, equalling Sergio Aguero's Champions League scoring record to put the holders in cruise control.
Although Man City were unable to increase their lead during a goalless second half, Man City have become the first team in major European competition history to net three or more goals in nine consecutive home games.
Victory for the Citizens has also seen them become the first-ever English club to win 10 Champions League matches in a row, and just the third side in the competition's history after Real Madrid (2015) and Bayern Munich (2013 and 2020).
In addition, City have extended their unbeaten home run in the Champions League to 30 games - an English record which is six matches clear of Arsenal's 24-game streak without losing set between September 2004 and April 2009.
The Citizens, who last tasted a Champions League defeat on home soil back in September 2018 against Lyon, are only eight games behind the all-time unbeaten home record in the competition set by Barcelona (38) between 2013 and 2020.
Man City have won an impressive 28 matches during their 30-game unbeaten home run, with Shakhtar Donetsk in the 2019-20 group stage and Sporting Lisbon in the 2021-22 last 16 the only two teams to prevent Guardiola's men from coming out on top.
After beating Copenhagen, Guardiola insisted that he does not take Man City's Champions League progression for granted, telling reporters: "For me, every time we get through in the group stages 'wow' because I know how difficult it is. I know how difficult it is.
"Everything is difficult. The Premier League is difficult, the FA Cup is difficult. People take it for granted now. It's good but we know internally, the manager and the players, that everything is difficult.
"This is what I want my club to feel, from the hierarchy, the people working here, the players - that everything is complicated. Still we are there in all competitions. It's really good."
Man City, who will discover their quarter-final opponents on March 15, turn their attention back to the Premier League title race with a top-of-the-table showdown away against leaders Liverpool up next on Sunday.