The Red Devils were awarded their 21st penalty of the season in the additional half hour, and Bruno Fernandes converted the spot-kick to earn a 1-0 victory.
Copenhagen put United's rearguard under pressure several times in the opening quarter of the match, but the English side's build-up play was a little more cohesive after the first water break. Mason Greenwood's clinical finish near the end of the half was ruled out due to a clear offside, but neither team deserved to take a lead into the interval.
Within 18 minutes of the second stanza, Greenwood and Fernandes both hit the woodwork with shots from the edge of the box, and later on Karl-Johan Johnsson made several excellent saves. But Copenhagen weren't merely defending for their lives, as they occasionally made inroads of their own, with ex-Everton full-back Bryan Oviedo - who was called off the bench - briefly causing problems down United's right side.
Johnsson thwarted Anthony Martial twice in the opening stages of extra time before Andreas Bjelland was penalized for a foul on United's busy French forward in the area. The keeper had made nine saves up until that point, and he went the right way for Fernandes' penalty. However, he was unable to block a savage effort from United's inspirational January arrival.
The game opened up, leading to more opportunities for Ole Gunnar Solskjaer's side. Copenhagen appeared to be drained of energy as the excellent Johnsson made four more saves to stop United from doubling their lead. The Swedish goalkeeper may attract some interest in the summer transfer market following his sublime display.
It was far from convincing from United, but their pursuit of a continental crown continues. The possibility of a titanic tussle between the Red Devils and Inter Milan in the final remains after the latter engineered a 2-1 |win over Bayer Leverkusen in Monday's other quarterfinal.