Zlatan Ibrahimovic, Lucas and Gregory van der Wiel were also on target for Laurent Blanc's side while Pierrick Capelle replied for Angers who are fifth in the table.
Unbeaten PSG, gunning for a fourth consecutive title, have 60 points from 22 games and lead second-placed Nice, who beat Lorient 2-1, by 24 points.
Monaco are third, also 24 points off the pace, ahead of the principality team's home match against Toulouse on Sunday.
Angers have 34 points, behind Stade Rennais on goal difference after the side from Brittany gave new coach Rolland Courbis a 1-0 victory over Gazelec Ajaccio in his first game in charge on Friday.
Nantes hold the record for the longest unbeaten streak in the league after going 32 matches without losing in 1994-95.
Angers looked lively in the opening half-hour but PSG took the lead in the 32nd minute when Ibrahimovic scored with a deflected low shot.
Lucas latched on to a cross to make it 2-0 in the 40th minute before van der Wiel added the third goal from point-blank range following excellent work by Ibrahimovic and Blaise Matuidi.
Capelle pulled a goal back for Angers with a vicious 20-metre shot but Di Maria netted in the 63rd minute with a delightful long-range volley.
The Argentine winger then completed the scoring with a half-volley in the 66th minute.
(Editing by Tony Jimenez)
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