After a run of 10 wins and one draw in 11 games since Solskjaer replaced the sacked Jose Mourinho in December, defeat is a reality check for United’s revival and they have a mountain to climb when the sides meet again for the second leg on March 6.
The English giants will also have to cope without Paul Pogba in three weeks’ time as he was sent off for two yellow cards a minute from time to round off a terrible night for the hosts.
The French champions have bowed out in the last 16 in each of the past two seasons to Spanish giants Barcelona and Real Madrid.
Yet, for all the positivity of United’s return to form in the past two months, they remain 14 points behind Premier League leaders Manchester City and Liverpool and the big rebuilding job required to make the three-time European champions contenders again for this competition was laid bare.
PSG showed they still retain plenty of world class talent despite their big name absentees as United struggled to contain the slick passing of Thomas Tuchel’s men in midfield and the pace of Mbappe in attack.
Angel di Maria was roundly booed by the home support on his return to Old Trafford after an unhappy one-season spell with United after signing for a then club record £60 million in 2014.
The Argentine nearly silenced his detractors with a dipping shot that flew just wide six minutes in.
PSG have struggled on the road in the Champions League against elite opposition but showed little sign of nerves as they stroked the ball around confidently.
– Injuries disrupt United –
However, it was when given the chance to counter-attack and use Mbappe’s speed they looked most dangerous.
The 20-year-old World Cup winner slotted a huge chance wide on the half hour mark, although Mbappe would likely have been ruled offside by VAR, on its introduction to the Champions League, even if he had found the net.
For all PSG’s injury problems, a double blow also rocked United in the seconds before half-time and at the break as Jesse Lingard and Anthony Martial limped off to be replaced by Alexis Sanchez and Juan Mata.
The home side never recovered their composure as PSG produced a stunning second-half display to all but book their place in the last eight despite David de Gea’s best efforts.
Mbappe had the first chance when his header was turned behind by the Spanish goalkeeper.
But from the resulting corner, Kimpembe was left completely unmarked to side-foot home from point-blank range.
A brilliant team goal doubled United’s trouble soon after when Mbappe was again too quick for Victor Lindelof and Eric Bailly to meet Di Maria’s low cross.
Thereafter only De Gea stood in the visitors’ way as he stayed big to block Mbappe’s attempted chip as he bore down on goal again before Juan Bernat’s rising drive was then diverted wide.
Any hope of a United comeback in Paris suffered another huge blow when Pogba was dismissed late on for catching Dani Alves with a raised boot.
PSG suffered the biggest collapse in Champions League history when Barcelona overturned a 4-0 first leg deficit to win the return leg 6-1 at this stage two seasons ago.
However, on this occasion PSG have done the hard work on the road making a similar comeback at the Parc des Princes even more unlikely.