Match ends, Manchester United 1, FC København 0.
Manchester United needed an extra-time penalty from Bruno Fernandes to finally see off a spirited FC Copenhagen and set up a potential Europa League semi-final against Wolves.
United were poor for much of the first half in the heat of Cologne but still had a penalty overturned and a goal ruled out by the Video Assistant Referee.
Ole Gunnar Solskjaer's side improved and dominated the second half but could find no way past inspired goalkeeper Karl-Johan Johnsson, with Fernandes and Mason Greenwood also each hitting the post and Marcus Rashford having another effort disallowed.
Fernandes finally broke through in familiar style, keeping cool to drive in United's 21st spot-kick of the season at the start of the extra period to extend their marathon season by another week.
Johnsson was magnificent between the posts for Copenhagen - ending the night with 13 saves as United rained down 26 efforts on goal all told - while the Danish runners-up failed to have a single shot on target.
United - who won this competition four seasons ago - will now face either Premier League rivals Wolves or Europa League specialists Sevilla in the last four in Dusseldorf on Sunday night.
- Follow reaction from Manchester United v FC Copenhagen, plus Inter Milan v Bayer Leverkusen
- Europa League 'final eight' begins - all you need to know
No way past for United
Three hundred and sixty-four days after Solskjaer started his first full season in charge of United, he is now two games away from a possible first trophy.
The January signing of Fernandes has already delivered a third-placed finish and Champions League football and the Portuguese midfielder was again the eventual difference maker on a draining night in scorching heat.
The temperature was still 32C at kick-off at 9pm local time and United made a poor start - Fred's error almost letting in Mohammed Daramy, before Brandon Williams had to head away from the goal-line.
But despite their lethargy, United always carried a threat and were briefly awarded a penalty for a shove at a set-piece before VAR flagged an offside in the build-up.
Greenwood finished brilliantly off the far post but the strike was correctly called back for another offside before Solskjaer witnessed a far better second half.
Greenwood fired against the post again, with his left foot this time, Rashford tapping in but again from an offside position before Fernandes thundered a shot against the opposite post from range.
Johnsson's individual showreel then threatened to throw a spanner in the works.
Perhaps the Swedish keeper's best save denied Anthony Martial, who eventually won the decisive penalty thanks to a push from former Brentford defender Andreas Bjelland.
Fernandes fired into the corner without his trademark hop on approach to ensure a 17th European semi-final for United.
Man of the match - Karl-Johan Johnsson (FC Copenhagen)
- 3BaillyBooked at 63minsSubstituted forLindelöfat 71'minutes
- 5MaguireBooked at 61mins
- 17FredSubstituted forMaticat 70'minutes
- 26GreenwoodSubstituted forMataat 90'minutes
- 18Bruno Fernandes
- 10RashfordSubstituted forLingardat 113'minutes
- 9MartialSubstituted forMcTominayat 120+1'minutes
- 1de Gea
- 2VarelaSubstituted forBartolecat 105'minutes
- 20BoilesenSubstituted forBengtssonat 15'minutes
- 16BielSubstituted forOviedoat 57'minutes
- 6StageBooked at 77minsSubstituted forMudrazijaat 105'minutes
- 10Gonçalves RodriguesBooked at 105mins
- 33Falk JensenSubstituted forBoving Vickat 111'minutes
- 11DaramySubstituted forKaufmannat 57'minutesBooked at 75mins
- 42Boving Vick
- Clément Turpin
- Shots on Target
Second Half Extra Time ends, Manchester United 1, FC København 0.
Substitution, Manchester United. Scott McTominay replaces Anthony Martial.
Foul by Nemanja Matic (Manchester United).
William Boving Vick (FC København) wins a free kick on the right wing.
Corner, FC København. Conceded by Victor Lindelöf.
Attempt blocked. Mikkel Kaufmann (FC København) right footed shot from the centre of the box is blocked. Assisted by William Boving Vick.
Substitution, Manchester United. Jesse Lingard replaces Marcus Rashford.
Brandon Williams (Manchester United) wins a free kick in the defensive half.
Foul by Karlo Bartolec (FC København).
Substitution, FC København. William Boving Vick replaces Rasmus Falk Jensen.
Paul Pogba (Manchester United) wins a free kick in the defensive half.
Foul by Robert Mudrazija (FC København).
Corner, FC København. Conceded by Harry Maguire.
Foul by Nemanja Matic (Manchester United).
Rasmus Falk Jensen (FC København) wins a free kick on the right wing.
Second Half Extra Time begins Manchester United 1, FC København 0.
First Half Extra Time ends, Manchester United 1, FC København 0.
Victor Lindelöf (Manchester United) hits the right post with a left footed shot from the centre of the box following a corner.
Attempt saved. Juan Mata (Manchester United) left footed shot from the centre of the box is saved in the centre of the goal.
- Food and mood: The link between what we eat and mental health
- Young shielders: What has isolation been like for them?