The game saw midfielder Paul Pogba sent off after suffering a second yellow card.
After the first half, PSG became clinical with two quick-fire goals to inflict pains on Solskjaer and his men who looked lost during the game.
The first came from Presnel Kimpembe who turned home at the far post from an Angel Di Maria corner at the 53rd minute. The second came from Kylian Mbappe finished who finished off from another assist from Maria in the 60th minute.
Manchester United are now left with a huge task to overcome as they head to Paris for the second leg.