Di Maria turned provider yet again 7 minutes later as he exploited the gaps left by Manchester United on the left wing as they pushed up searching for an equalizer to tee up Kylian Mbappe for the French team's second of the night.
Tuesday's loss was the first United had suffered under Solskjaer's reign.
Incidentally, as it would turn out, it was also their heaviest defeat at Old Trafford in European competition history. We all are very optimistic and positive, it's just one result and we're in a good moment.
It would have been more but for some fine goalkeeping from David de Gea.
The English giants will also have to cope without Paul Pogba in three weeks' time as he was sent off a minute from time to round off a awful night for the hosts. Momentum can take a team only so far and Tuchel, the highly rated former Borussia Dortmund coach, showed the need to be tactically astute to win on a stage as unforgiving as the Champions League knockout rounds.
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'Man United played at home and had one shot on goal in a Champions League game - that tells you about the difference between the two teams'.
In the night's other last-16 game, teenager Nicolo Zaniolo scored twice to lead Roma to a 2-1 victory.
Wenger was also critical of United at half-time, before they had even conceded, saying: 'We predicted Man United's problems before the game.
"The first goal is always going to be important and the way we concede it is disappointing", added Solskjaer.
Manchester United finished second in Group H and shuddered in December when UEFA pitted them against Group C victor PSG in the Round of 16 draw, which took place in December.
The Red Devils moved into the top four for the first time this season after a 3-0 win against Fulham at Craven Cottage on Saturday.
Angel di Maria was roundly booed by the home support on his return to Old Trafford after an unhappy one-season spell with United after signing for a then club record £60 million in 2014.