PSG, who are bidding for a fifth successive French title, moved level on 74 points with Monaco, having played a game more than the front-runners who are at home to second-bottom Dijon on Saturday. Angers stayed 12th on 39 points.
The visitors, who were missing several regular starters, were made to work hard for their win as goalkeeper Kevin Trapp produced a pair of superb saves at crunch moments.
The keeper kept out a swerving Nicolas Pepe effort before Argentina winger Di Maria fired PSG ahead with a sublime 28th-minute free kick, curling his shot from 25 metres into the bottom left corner.
Read the full article on eurosport.co.uk: Di Maria double keeps PSG on Monaco's tail