Mauricio Pochettino, who won his first trophy for PSG this week, was unavailable after testing positive for Coronavrius but Neymar Junior started for the first time since returning from injury.
Angers threatened a breakthrough with just two minutes in from a curling attempt by Pierrick Capelle on the right-side of the area, but PSG goalkeeper Keylor Navas tipped over the bar.
Neymar was brought into action for the first time following the half-hour mark when he send a cutback from Angel Di Maria into the side-netting.
Italian Moise Kean managed to get on the ball late in the first half from a cross by Di Maria off good spade work from Kylian Mbappe, but the on-loan forward fluffed the opportunity.
Kean reversed roles early in the second half when he released Mbappe with a ball into the area, but the Frenchman slammed into the side-netting from the left-side of the area.
Mbappe was set through again minutes later from a one-two involving Neymar, but Angers goalkeeper Paul Bernardoni's finger-tips denied the forward.
Angers made a substitution inside the 61st minute, as Cameroonian international Stephane Bahoken came on for Lois Dony with the balance of play delicately poised.
However, the Parisans secured the lead through Layvin Kurzawa ten minutes later with a superb first-time strike from a cross on the right by Alessandro Florenzi.
Angers staged a late surge towards a turnaround, but the table-topping Parisans ran down the closing seconds to ensure victory.