Pinpoint delivery from a corner by the man who cost United a then-British record £59.7m when he arrived from Real Madrid in 2014 led to Presnel Kimpembe escaping Matic and volleying home at the far post.
Incidentally, as it would turn out, it was also their heaviest defeat at Old Trafford in European competition history.
Zaniolo continued his superb breakthrough season by finding the net twice in six second-half minutes before Adrian Lopez pegged one back in the 79th minute.
Former United winger Di Maria, booed from the outset by sections of the crowd, had the last laugh when he collected a fine pass from Marquinhos and set up Mbappe for the second goal. "Maybe he was a bit nervous and a bit overused because he plays all the time for us".
United was forced to adapt, too, after losing Jesse Lingard and Anthony Martial to injury for the second half.
The English giants will also have to cope without Paul Pogba in three weeks' time as he was sent off for two yellow cards a minute from time to round off a awful night for the hosts.
United will have it all to do in the second leg as none of the previous 34 teams to lose a home first leg of a Champions League tie by two or more goals have ever progressed.
But having come off the bench to score the victor in the 93rd minute of the 1999 final against Bayern Munich, Solskjaer is the man who epitomised more than most the "never say die" attitude of many Sir Alex Ferguson Manchester United teams.
AS Roma 2 (Nicolo Zaniolo 70', 76') FC Porto 1 (Adrian Lopez 79') HT: 0-0.
Wenger was also critical of United at half-time, before they had even conceded, saying: 'We predicted Man United's problems before the game.
Having a good run in the Premier League is one thing, but doing it against the big boys at the sharp end of the Champions League is something else. It has to be one that we are going to learn from.
The 20-year-old World Cup victor slotted a huge chance wide on the half hour mark, although Mbappe would likely have been ruled offside by VAR, on its introduction to the Champions League, even if he had found the net.
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.