The winger's corner was volleyed in by Presnel Kimpembe for his first PSG goal in the 53rd minute.
PSG lost 5-2 on aggregate to Real Madrid in the last 16 a year ago and in 2016-17 they were on the end of one of football's greatest ever comebacks, Barcelona overturning a 4-0 first-leg deficit to progress. "But considering how many players we were missing and others not in great shape, it was great to win here in these circumstances".
The Norwegian had won 10 of his 11 games in charge of United before their defeat against PSG.
Eric Bailly and Victor Lindelof both had a significant head-start on the World Cup winner as they sprinted back towards goal, but Mbappe outpaced both of them to tap home Di Maria's cross.
"We are going to have to go down there, believe in ourselves, play a good game and improve from today obviously".
Solskjaer has passed all of the tests he has faced as United manager with flying colours so far, but there are still no signs of him getting the job full-time, however were he to negotiate a path into the quarter finals of the Champions League, it would be nearly impossible to deny him the opportunity to become the permanent successor to Mourinho.
"Slip up in those fixtures, lose ground on the top four and there will be doubts as to whether Solskjaer is the man to challenge Liverpool and Manchester City for the title next season".
"We need to stop with the scare stories".
Di Maria, whose every touched was booed by the United fans following the manner of his departure from Old Trafford in 2015, then set up Kylian Mbappe seven minutes later.
Alexis Sanchez was introduced at the beginning of the second half but was once again unable to impose himself as his struggles in a United shirt continued.
Solskjaer was in no mood to pull his punches with the Chilean, saying: "I can't do anything about Alexis Sanchez". He needs to play with a good mindset and to be positive. We were not used to it. "I am very happy and proud to have scored my first goal, but I am even happier with the win".
"I'm disappointed, of course, that we're not going to have Paul in the next round because I thought he was our best player".
"It's always unsafe for him from the corners and of course a superb assist, it was a ideal pass for Kylian".