Manchester City kept their quadruple hopes alive after coming back from two goals down to win 3-2 at Swansea City in the FA Cup quarter-finals thanks to Sergio Aguero’s controversial late header.

Pep Guardiola’s men looked to be heading out of the competition at the hands of second-tier opposition, but three goals in the final 21 minutes saw City come back from the brink, as Aguero – who appeared to be offside – nodded in the late clincher.

City made a fine start and went close three times in the first 15 minutes, but Swansea capitalised soon after – Grimes coolly dispatching a penalty after Fabian Delph tripped Connor Roberts.

It was 2-0 before the half-hour mark as Swansea brilliantly carved through City and Nathan Dyer teed up Celina, who found the top-right corner with a curling effort from just inside the box.

The Citizens were back in it in the 69th minute when substitute Aguero saw a shot come back off Jay Fulton’s face and the Argentina striker subsequently teed up Silva for a fine outside-of-the-foot finish.

Guardiola’s side were level 12 minutes from the end, with Aguero’s penalty – after Cameron Carter-Vickers was adjudged to have tripped Raheem Sterling – coming back off the post and going in off the unlucky Nordfeldt.

With City piling on the pressure, there was an air of inevitability about the winner, which arrived when the prolific Aguero met Silva’s cross with a well-placed header into the bottom-left corner.