City knew a win would seal its place in the round of 16 with two games to spare, but it endured a frustrating Wednesday (AEDT) at Parken.

Rodri had a goal disallowed for a handball by Riyad Mahrez, who then had a spot-kick saved by Kamil Grabara before Gomez was dismissed for a professional foul in an eventful first half.

Erling Haaland was an unused substitute as City's six-game winning run came to a halt and they lost its 100 per cent Group G record, but it remains on the cusp of qualifying for the next stage.

Rodri rifled a thunderous long-range strike into the top-left corner in the 11th minute, but referee Artur Dias ruled the goal out for a Mahrez handball after a being instructed to look at the pitch-side monitor.

Mahrez wasted a chance to make amends from the spot after Nicolai Boilesen was adjudged to have handled following another VAR check, but Grabara dived to his left to deny the winger midway through the first half.

There was another big blow for City on the half-hour mark, when Dias was once again summoned to the touchline and the busy Portuguese official deemed that Gomez had pulled Hakon Haraldsson down to deny him a goalscoring opportunity.

Pep Guardiola's side was dominating possession despite being a man down and Grabara punched away a Kevin De Bruyne strike early in the second half.

Isak Johannesson came agonisingly close to Victor Kristiansen's teasing cross from the left at the other end as Copenhagen scented a famous victory.

Grabara produced more heroics by diving to his right and palming away Joao Cancelo's drive as neither side could fashion a winner.