Di Maria beat Real goalkeeper Thibaut Courtois at his near post to put PSG ahead in the 14th minute, but it was his second goal just after the half-hour that really lit up this encounter.
Thomas Tuchel's men, who lost at Rennes last time out, have seen the start of their season dominated by the Neymar transfer saga.
While PSG have crashed out at the last-16 stage in Europe each of the past three years, it is almost unfathomable they could be dethroned in France.
French World Cup-winner Kylian Mbappe also apologised for sparking speculation about his own future at the club.
In the absence of Neymar, the Brazilian who is still working his way back to full fitness, the French starlet Mbappe was the focus of attention.
The 20-year-old World Cup winner suggested that he could be ready to leave PSG after just two seasons.
The 20-year-old made the switch from Monaco to PSG for 180 million euros in 2017.
The 20-year-old backed up his excellent 2018 World Cup, where he scored four times as France won the trophy, by netting 38 times for PSG this season.
Mbappe, PSG's gifted 20-year-old striker, lunged with his studs into the knee of Rennes defender Damien Da Silva near the close of extra time on Sunday.
The France star caught the Rennes defender on the knee with his studs, and can expect a lengthy ban.
Mbappe took his league tally for the season to 30 following his treble on Sunday, which came just hours after PSG were crowned champions for the sixth time in seven years.
Marcus Rashford's 94th-minute penalty at the Parc des Princes gave United a 3-1 win in France to send the English club through on away goals.
Anelka said to him it was "not a surprise" that PSG cruised to a 2-0 victory at Manchester United in the first leg.
A week after reaching a half-century of goals in France's top flight at the age of 20, Mbappe netted a penalty for the first time in his Ligue 1 career just before the hour mark.
Kylian Mbappe's record-breaking run, Lionel Messi being Lionel Messi, Cristiano Ronaldo's struggles and more.