The match started with the Parisians swarming into the opposition territory with clear intentions of grabbing an early lead.
PSG dominated but needed an own goal from Angers right back Issa Cissokho, brother to Aston Villa defender Aly, in stoppage time to prevail at the Stade de France.
Angers, playing in the final for the first time since 1957, escaped in the first half when Angel Di Maria‘s deflected cross hit the post.
The capital side missed a number of chances to take the lead in the opening 45 minutes, Edinson Cavani in particular guilty of wasting some fine opportunities, but the holders, who have now won the competition three years in a row, eventually got their goal in the 91st minute when Cissokho headed into his own net following a corner from Di Maria as the 100th final passed the 90-minute mark with Cissokho.
Emery has been under intense pressure after a disappointing first season at the Parc de Princes, with PSG finishing eight points behind Ligue 1 champions Monaco and exiting the Champions League in the last 16.
According to BBC Sport Victory at the Stade de France ensured they will end the season with two trophies, having beaten Monaco 4-1 in the French League Cup final in April.
PSG has now surpassed Marseille as the club with the most French cups.