anchester United's Champions League campaign is hanging in the balance as two goals from Neymar helped Paris St-Germain secure victory at Old Trafford.
Marcus Rashford had cancelled out the Brazilian's early opener with his third goal in four games against the French outfit.
But Marquinos' excellent second-half finish put the visitors back in front and after United midfielder Fred had been sent off for a foul on Ander Herrera, Neymar tapped home his 38th Champions League goal.
The result leaves United level with PSG and RB Leipzig on nine points in Group H and knowing they need a draw away to the German side next Tuesday to progress to the last 16.
Rashford pain, Neymar gain for PSG
In the build-up to the game, PSG boss Thomas Tuchel admitted Rashford had become "a little bit annoying".
The sentiment was perfectly understandable given two seasons ago the England forward scored the injury-time penalty that knocked PSG out, even though they had won the first leg of their last-16 tie 2-0 at Old Trafford.
Rashford was also responsible for United's 87th-minute winner in the French capital on matchday one.
So it is fair to assume Tuchel's view only hardened when Rashford's shot - after Kaylor Navas had pushed away an Anthony Martial effort - completely wrong-footed the keeper and ended up in the bottom corner.
The goal equalised Neymar's well-taken sixth-minute effort and took Rashford's tally in this season's competition to six, level with the likes of Erling Haaland and former United team-mate Romelu Lukaku.
Had Martial not blazed over when presented with an open goal when the second half was still in its infancy, or had he finished off the rebound when Edinson Cavani's delicate chip came back off the crossbar, rather than blast it into Marquinos, PSG might have had the life sucked out of them.
As it was, they were the ones building up a head of steam when Ander Herrera's off-target shot was turned into Marquinos' path and he put them back in front.
United did push for an equaliser and substitute Paul Pogba came close when he volleyed over from the edge of the area but, with an extra man, PSG always had the edge and after Kylian Mbappe had fired wide, Neymar finished the hosts off.
With 38 goals he is now two behind Sergio Aguero, who is the second highest South American goalscorer in the competition.
Solskjaer's big mistake
Major question marks will hang over Solskjaer after this result.
While the United boss can legitimately argue the caution that got Fred sent off was debatable - he screamed for a VAR check but they do not intervene on yellow card decisions - he can barely claim the Brazilian did not deserve to be sent off at some point in the game.
The biggest flashpoint came when he clashed with Leandro Paredes shortly before Rashford's equaliser.
As the pair faced off, Fred appeared to push his head towards Paredes, who went down clutching his face. Italian referee Daniele Orsati went to the screen to check what had happened but, to Tuchel's disbelief, only issued a yellow card.
When the same pair came together again shortly afterwards, Orsati ruled Paredes was the aggressor and cautioned him, even though Fred ended up standing on his opponent.
Given an angry Neymar went to the referee for a long chat at half-time, after he was pulled away from Scott McTominay, it felt an obvious decision to replace Fred, particularly as Solskjaer had five substitutes at his disposal.
Instead, Fred returned for the second period, leaving his manager to face the consequences, with PSG's official Twitter feed announcing 'finally' as the Brazilian made his way prematurely to the dressing rooms.
Prolific Rashford but poor home form - the stats
The away side have won all four Uefa Champions League matches between Manchester United and Paris St-Germain. Excluding games played at neutral venues, it's the first fixture in the competition's history to see the first four meetings all won by the away side.
Manchester United have now lost more of their eight home games in all competitions this season (4) than they did in 28 matches at Old Trafford last term (3).
Manchester United have lost four of their past seven Champions League home games (W3), as many as in their previous 52 matches beforehand.
PSG have won both of their past two away matches against English opposition in all competitions (both v Man Utd); they had only won one of their first 10 such visits before this (D4 L5).
Both of Manchester United's last two Champions League red cards have come at home to PSG (Pogba the other in February 2019) - their only two such meetings with the French side.
Man Utd's Fred was the 49th different Brazilian player to receive a Champions League red card; only France has had more different players sent off in the competition's history (55).
At 05:45, Neymar's opener for PSG was the earliest Champions League goal conceded by Manchester United since September 2015, when Daniel Caligiuri scored against them after 03:53 for Wolfsburg.
Since his Uefa Champions League debut in 2013, only Cristiano Ronaldo (79), Robert Lewandowski (60) and Lionel Messi (59) have more goals in the competition than PSG's Neymar (38). However, his double was the Brazilian's first goals in his six Champions League matches away to English clubs.
Marcus Rashford has scored more goals in five Uefa Champions League games for Man Utd this season (6) than he managed in 18 appearances in the competition across his two previous seasons, 2017-18 and 2018-19 (5).
Rashford is the first Man Utd player to score in all three of their home games in a single group stage in the Uefa Champions League since Ruud van Nistelrooy in 2004-05. Indeed, he is just the second Englishman to score six Champions League goals in a single group stage for any side, after Harry Kane in both 2017-18 and 2019-20 (six in both).
Manchester United travel to West Ham in the Premier League on Saturday (17:30 GMT). That game is set to be the first top-flight match to have fans since March.