Angers had taken twice as many points from their last five Ligue 1 games than PSG had managed, but it was the recently crowned champions who came out on top thanks in large part to the work of Neymar.
A week on from scoring his 50th goal for the club, the Brazilian forward broke the deadlock with a diving header 20 minutes in before teeing up Angel Di Maria just before the hour.
PSG held on to put an end to their three-match winless run, despite having Marquinhos sent off and conceding a late goal from Flavien Tait.
Brought back into the side after missing the draw with Nice last week, PSG goalkeeper Gianluigi Buffon produced fine saves to keep out Tait and Stephane Bahoken in the opening 16 minutes of the match.
But the visitors had chances of their own in a lively start as Edinson Cavani was denied by Ludovic Butelle and then had a goal rightly ruled out for offside.
The Parisians made their spell on top count as Dani Alves delayed his cross and picked out Neymar, who guided the ball away from Butelle with a header into the bottom corner.
After plenty of toiling from Thomas Tuchel's side, Neymar set up the second after 58 minutes by drifting past Vincent Manceau and clipping the ball into the centre of the box for Di Maria to easily head home.
Tait converted at the second attempt following Buffon's save from his late penalty, awarded after Marquinhos brought down Wilfried Kanga in the box, but PSG held firm for the win.