Juan Bernat soon equalised for the hosts, but Lukaku capitalised on a second costly error to restore United's lead before Marcus Rashford scored a controversial VAR-awarded penalty in the 94th minute to complete an unprecedented turnaround.
Here, Sports Mole rates and slates the PSG players as they suffered elimination at the last-16 stage of their most coveted competition for the third successive season.
Gianluigi Buffon: If this is to be his final Champions League game then it was not a fitting way for one of the all-time greats to bow out. Has still never lifted this trophy, and his failure to do so this year is partly down to his fumble at the feet of Lukaku which gifted United their second goal. (5/10)
Thilo Kehrer: Was at fault for United's first with a careless back-pass which sent Lukaku in on goal. That early opener gave United the glimmer of hope they needed and without it they may not have gone on to achieve what they did. (4/10)
Thiago Silva: Could do little about any of the goals as the errors came from elsewhere. Made a couple of crucial interceptions, but it was ultimately in vain and perhaps PSG needed more of a kick from their captain to kill the tie off. (6/10)
Presnel Kimpembe: Unfortunate to concede the telling late penalty. Jumped with his back to the ball and could not do much to prevent it hitting his arm. Otherwise a solid performance. (6/10)
Dani Alves: Slid a couple of nice passes down the channel for Mbappe during the first half and had one or two sights of goal himself which went begging. Less effective in the second half, though. (6/10)
Marquinhos: Provided the base from which PSG could build while on top in the first half. Helped the hosts to dominate possession throughout and ultimately their failure to make that count is not down to Marquinhos. (6/10)
Marco Verratti: Typically combative in the middle of the park. His tackles and intensity were as big a reason as anything for PSG dictating the tempo. (7/10)
Juan Bernat: Scored PSG's goal and perhaps should have had another, only to put that second attempt too close to David de Gea. Was part of a double-act which toyed with United's right flank in the first half. (8/10)
Julian Draxler: Forced off in the second half with a hamstring injury. Most of PSG's attacks came down the opposite flank, so Draxler had less opportunity to show what he could do. (6/10)
Kylian Mbappe: Not one of his finest matches, but even then he produced a few moments of brilliance. Provided the assist for PSG's goal - and an exquisite second for a disallowed effort - while his pace was a constant danger to the United defence. (7/10)
Angel Di Maria: United's main tormenter during the first half as he took Eric Bailly to the cleaners. Ultimately could not turn good positions into goals for his side, but his quality was once again plain to see against his former club. (7/10)
Leandro Paredes: Came on as part of a double change with 20 minutes remaining but could do nothing about what followed. (6/10)
Thomas Meunier: Was an upgrade on Kehrer and may have been expecting his chance to come sooner than the 70th minute after Kehrer's poor first-half display. (6/10)
Edinson Cavani: Introduced as one last throw of the dice in the 95th minute but barely had a touch of the ball. (6/10)