Zlatan Ibrahimovic bagged a brace for the capital club to inspire a first league win of the season.
Despite their big spending PSG had only managed to draw their opening three Ligue 1 matches - including goalless encounters in their previous two.
But Ibrahimovic, a 20million euro summer buy, ensured there was no repeat as he latched onto Maxwell's through-ball to score after just 27 seconds.
Although Aurelien Chedjou equalised from a corner on 11 minutes Ibrahimovic, who scored has now scored all his side's league goals this season, poked home the winner just before the half-hour.
"It was a good display," said Ancelotti. "It was a very difficult game.
"We will keep on working hard and I think this win is very promising for the future. There is still room for improvement, but we played like a team."
The victory will go some way to easing the pressure on the Italian coach, for whom the Ligue 1 title is a minimum requirement this season after missing out to Montpellier last term.
The three points leave PSG in eighth place, six adrift of leaders Marseille, and Ibrahimovic admitted the win was long overdue.
"It was a good game that we needed to win for the confidence," the Sweden international said.
"In the previous matches this season, we haven't had that little slice of luck. It was very important to get the three points.
"On a personal note, I'm still not 100%, but when I'm out on the pitch, I give the absolute maximum.
"There are 11 of us out on the pitch, and when we win, it's as a team."