The Uruguayan aimed from close range at the bottom corner, but Ludovic Butelle reacted quickly to prevent the PSG forward from opening the scoring.
Three minutes later, though, Mbappe was on target as he drilled the ball into the back of the net after latching on to a perfectly-weighted pass.
Just a quarter of an hour into the match, PSG were restricted to 10 men due to a stamp from Thiago Motta on Romain Thomas, who was left with a huge gash across his chest.
The midfielder could have zero complaints about the straight red card, but the dismissal did little to trouble the home side as Mbappe netted his second goal of the night after being set up by Layvin Kurzawa.
After the half-time break, Angel Di Maria tried his luck from just outside the penalty area, but one of his own teammates prevented it from reaching the net as he inadvertently blocked the path of the ball.
With just over five minutes left on the clock, Mbappe missed an opportunity to nab a hat-trick when his shot from inside the danger area ratted off the post.
In the end, PSG recorded their eighth league win on the bounce, while also ending Angers's three-match unbeaten run.
PSG XI (4-3-3): Trapp; Alves, Silva, Kimpembe, Kurzawa; Verratti, Motta, Draxler (Nkunku 76'); Mbappe, Cavani (Rabiot 58'), Di Maria (Lo Celso 68')
ANGERS XI (4-1-4-1): Butelle; Manceau, Thomas, Pavlovic, Bamba; Santamaria; Tait, Coulibaly (Guillaume 78'), Mangani, Ketkeophomphone (Toure 58'); Kanga Aka (Ekambi 58')