The result put the capital side on 77 points, leading second-placed Olympique de Marseille, who beat Nantes 3-2, by 15 points with five games left.
Should PSG avoid defeat at the Parc des Princes against RC Lens on Saturday, they will clinch the title that puts them level on 10 with St Etienne, who won their titles between 1957 and 1981.
Stade Rennais are third on 56 points after losing 2-1 at Racing Strasbourg, who are now fourth behind them on goal difference.
Also on 56 points are fifth-placed Monaco who beat Nice 1-0 at home.
The top two qualify directly for the Champions League group stage while the third-placed side will play the third qualifying round.
With Lionel Messi and Marco Verratti missing the game through injury, PSG were still a cut above at Angers.
Mbappe Decisive Goal Opens Scoring
Mbappe put them ahead with his 22nd league goal of the season as he fired home a low shot from just outside the box that Anthony Mandrea could only touch with the tip of his gloves on 28 minutes.
Nine minutes later, Angers threatened with Mohamed-Ali Cho's strike hitting Keylor Navas's post.
But PSG doubled their tally on the stroke of halftime when Ramos headed home from Angel di Maria's cross.
Marquinhos put the result beyond doubt in the 77th minute with a header from another perfect cross by Di Maria, who started in the absence of Messi.
PSG finished with 10 men after substitute Edouard Michut was sent off for a brutal tackle on Romain Thomas.
In Marseille, OM knew that they needed to win to delay PSG's title celebrations and they twice came from behind to do so.
The visitors opened the scoring when Andrei Girotto headed home after 26 minutes, only for Dimitri Payet to level 13 minutes later with a penalty following a foul by Nicolas Pallois on Boubacar Kamara.
Pallois, however, made up for his mistake with a superb whipped cross that was cleared into the path of Marcus Coco, who found the back of the net with a fine volley one minute from the break.
Payet equalised with another penalty after a foul by Fabio Da Silva on Cedric Bakambu in the 55th minute.
Backed by a raucous crowd, Jorge Sampaoli's side effectively wrapped it up in the 75th when Amine Harit found the back of the net with a low shot from Gerson's cutback.
Elsewhere, RC Lens beat Montpellier 2-0 at home to cement seventh place. They have 53 points and trail sixth-placed Nice by one point.