Injuries to Anthony Martial and Jesse Lingard dented United's attacking thrust and PSG scored twice in seven second-half minutes at Old Trafford on Tuesday to put a foot in the quarter-finals.
Presnel Kimpembe converted a corner from Angel Di Maria to score his first professional goal and the former United winger recorded another assist when he set up Kylian Mbappe for a crucial second.
Although PSG were without injured forwards Neymar and Edinson Cavani, United could muster no response with veteran goalkeeper Gianluigi Buffon completely untested and the Premier League side's task in next month's second leg looks huge, especially as Pogba will be banned.
Di Maria bent an early curler wide on his Old Trafford return then Mbappe missed the target after being sent through on goal by Julian Draxler's incisive pass.
United lost both Martial and Lingard to injury with Alexis Sanchez coming on moments before the interval and Juan Mata introduced for the second half.
David de Gea was tested for the first time in the 53rd minute, diving low to his left to push away Mbappe's header, but PSG opened the scoring from the resulting corner.
Di Maria's right-wing delivery curled over Pogba and Kimpembe shook off the attentions of Nemanja Matic to send a controlled volley into the roof of De Gea's net.
PSG almost scored a quickfire second when a thumping drive from Dani Alves flew just wide but they extended their advantage with a potentially pivotal second on the hour.
Di Maria was again the creator, finding too much space on the left wing to deliver a low cross that Mbappe finished superbly after powering through a gap in the middle of United's defence.
Solskjaer waited until the 84th minute to send on Romelu Lukaku but PSG held on comfortably, with United's misery complete when Pogba was shown a second yellow card for a foul on Alves.