Angers boasted an excellent defensive record heading into the game, but had little answer once star striker Zlatan Ibrahimovic put PSG ahead in the 32nd minute.Di Maria capped an outstanding performance with two goals midway through the second half, after Brazilian winger Lucas and right back Gregory van der Wiel had scored either side of halftime.
Di Maria received a standing ovation when he left the field 20 minutes from time, with Edinson Cavani replacing him.
Midfielder Blaise Matuidi set up three goals for PSG, which has won 19 games and drawn three this season and has a massive goal difference of 46.
"It's the first time I've set up three goals, but I'm more happy with the way we played collectively," Matuidi said. "There's a lot of talent in this team, as you can see with Angel and Ibra(himovic). I try to keep up with them, but it's not easy."
PSG's Gregory van der Wiel, center, celebrates with Zlatan Ibrahimovic after scoring, during the …
Nice rallied to beat Lorient 2-1 at home later Saturday with another solo goal from winger Hatem Ben Arfa, and is level in second place with Monaco. But Monaco can reduce PSG's lead to 21 if it beats Toulouse at home on Sunday.
PSG's last league defeat was away to Bordeaux on March 15 last season — and it finished last season in style with nine straight wins, meaning that PSG has not lost for 31 league games in total.
Saturday's win was also PSG's 11th straight in all competitions — equaling the club record.
"We said before the game not to give them anything, but that's exactly what we did," Angers midfielder Pierrick Capelle said. "When you give a team like that anything, they take advantage straight away."
In a subdued atmosphere at the Parc des Princes, the home crowd had little idea what was to follow during a dull opening spell.
PSG finally clicked into gear midway through the half when Di Maria played a clever pass behind the defense and Van der Wiel forced a near-post save from goalkeeper Alexandre Letellier.
Letellier, who played for PSG's youth teams and reserves, then denied Matuidi after narrowing the angle well. He had a fine game and prevented a bigger rout.
Although he was powerless to stop Ibrahimovic's league-leading 17th goal, Letellier was also a bit unlucky as the Sweden forward's angled strike took a deflection.
Lucas made it 2-0 shortly before the break when he finished from close range after Di Maria back-heeled the ball to Van der Wiel, who then flicked it to Lucas from the byline.
Van der Wiel got a rare goal in the 54th, volleying in from near the penalty spot after Matuidi had volleyed over a neat pass from the left at full stretch.
With PSG slacking off a bit, Capelle made it 3-1 with a deflected strike from the edge of the penalty area.
Then it was all Di Maria in a spell-binding few minutes that must leave Manchester United's beleaguered fans baffled as to why coach Louis van Gaal sold him in the summer.
Di Maria's first goal was even better than Van der Wiel's, as he collected a lofted pass from Lucas, and beat Letellier with a delightful curling lob in the 63rd, despite being off balance when he struck the ball.
Just three minutes later, the Argentina winger ran onto a fine pass from Matuidi and waited for Letellier to come off his line, before dinking the ball over his head with the supreme confidence of a player in top form.
"We know the quality of their players, so it's not even surprising when you see them do things like that," Letellier said.
Since joining from United, Di Maria has eight goals in 16 league games. His previous best goal tally was seven for Real Madrid during the 2012-13 season.
Ibrahimovic almost made it 6-1 near the end, but Letellier tipped over his dipping free kick.
Also Saturday, it was: Lille 1, Troyes 3; Montpellier 1, Caen 2; Guingamp 1, Bastia 0; and Nantes 2, Bordeaux 2.
Furious Bastia players confronted referee Mikael Lesage after he awarded Guingamp a 94th-minute penalty and sent off two players from the Corsican side, while Bordeaux scored in the 84th and then equalized in injury time.
Troyes secured its first win of the season thanks to two goals from impressive striker Jimmy Cabot, who also set up the third goal, but remains in last place — 11 points away from safety.
In Sunday's other games, Reims faces Saint-Etienne and Lyon takes on Marseille.
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