Fullback Kurzawa volleyed home for his first goal of the season, allowing PSG to move onto 42 points from 20 games, two ahead of Olympique Lyonnais, who host Metz on Sunday.
"All due respect to Nimes, we are Olympique de Marseille. We're supposed to be aiming at a Champions League spot and we cannot play that kind of game," said defender Alvaro Gonzalez.
In Angers, PSG were without coach Mauricio Pochettino, who has been isolating since Friday after testing positive for COVID-19.
Angers were the most dangerous side early on while Kylian Mbappe, who has not scored in his last four competitive games, struggled to find his pace and Angel Di Maria was missing in action on a terrible pitch in driving rain.
PSG failed to muster a shot on target in the first half.
The visitors were equally unimpressive after the interval but Kurzawa came to their rescue with a volley from Alessandro Florenzi's cross in the 70th minute.