United knew a point would be enough to secure a place in the round of 16 and they really should have wrapped the game up well before Marquinhos put PSG 2-1 up in the 69th minute and Fred received his marching orders a minute later.
It was surprising Fred was still on the field by that stage having received only a yellow card following a VAR review of an off-the-ball head-to-head clash with Leandro Paredes.
The pair were involved in a strong challenge later in the first half for which Paredes was booked but despite having plenty of options on the bench, United manager Ole Gunnar Solskjaer decided against substituting Fred, a costly mistake.
United created several good chances after the break but failed to go ahead.
Cavani was sent through and launched an audacious chip over the advancing Navas but the ball struck the crossbar -- Martial's follow up shot was brilliantly blocked by Marquinhos.
The defender struck the bar himself with a looping header over David De Gea and the goalkeeper pulled off a great save to keep out a low shot from substitute Mitchel Bakker.
Then came the minute that changed the game -- a half-cleared corner rattled around the box before it was poked in by Marquinhos.
Fred was dismissed after a foul on ex-United midfielder Ander Herrera as things fell to pieces for the home side.
Paul Pogba was thrown on and went close with a superb volley from outside the area but as United threw men forward they left holes at the back.
Mbappe powered through with a speedy run from deep but side-footed wide before the outcome was settled when Rafinha set-up Neymar for a simple tap-in.
PSG now have the head-to-head advantage over United and the easier task on paper next week while Solskjaer's men have plenty to do in Leipzig.