Evian have previous for springing surprises against PSG, having beaten them in the Coupe de France and Ligue 1 in recent years, and again frustrated the champions on Friday, with Yohan Cabaye's second-half dismissal compounding Laurent Blanc's woes.
The visitors were missing influential striker Zlatan Ibrahimovic, Thiago Motta and captain Thiago Silva, with the absence of the former in particular proving decisive in a first half of few chances.
Having shipped six goals to Rennes in their last outing, Pascal Dupraz's defence were in much better shape on their return to Annecy and were boosted by Cabaye picking up a second yellow card shortly after the hour.
With a man advantage, the hosts saw out the draw to pick up their first point of the new campaign as PSG's stuttering start to their quest for a third-consecutive league title continues.
Blaise Matuidi's burst and cross from the left spelt danger for Evian in the opening five minutes before the hosts managed to clear as PSG quickly settled into their rhythm.
However, Blanc's men struggled to break down an Evian side who appeared more than happy to sit deep and allow their opponents plentiful possession.
Cavani's tame 25-yard free-kick marked the visitors' first attempt on target after 22 minutes shortly before Nicki Bille Nielsen's dipping set-piece effort threatened Salvatore Sirigu at the other end.
PSG continued to dominate possession after the break but frustration was evident among Blanc's men as Cavani was adjudged offside, having been sent through on goal, before Cabaye picked up a second yellow card.
A late challenge on Bille Nielsen saw him sent off for the first time in a PSG shirt to sum up a disappointing night for the Parisians.
Cavani and Nicolas Benezet had opportunities for either side late but it ended goalless as Evian again shocked the title holders at the Parc des Sports.
