Beckham was handed the captain's armband for the Ligue 1 champions-elect and the England legend impressed against their already-relegated opponents.
The 38-year-old may yet play in PSG's final game of the season against Lorient next Sunday, but he made an emotional farewell to the Parc des Princes.
Beckham hugged his team-mates before being replaced by Ezequiel Lavezzi eight minutes from time, while club president Nasser Al-Khelaifi also shed a tear.
"I want to say thank you to everybody in Paris. To my teammates, to the staff, to the fans," said Beckham, who hopes to stay involved with PSG.
"It's been very special to finish my career here. It could not have been any more special.
"I just feel that it's the right time. I feel that I've achieved everything that I could in my career. I wanted to go out as a champion.
"I've finished my career in a team that has treated me like I've been here for 10 years.
"After 22 years of playing football I'm going to take a few months to enjoy time with my family.
"It's been a very special place for me."
Zlatan Ibrahimovic scored either side of Blaise Matuidi's goal to secure the win for PSG.
Asked whether he could feature next weekend, he replied: "We'll see. There's a plastic pitch next weekend. I ruptured my Achilles a few years ago, so it's not great for it. Like I said, tonight was very special. I'll be part of the team next week. Whether I play or not, who knows?"
Beckham was particularly touched by the honour of skippering the team and said he would be forever grateful.
"That started my emotions kicking in earlier today, when the manager called me in and said 'we've spoken to the players, it's the players' idea - we want to make you captain'," the former England captain told Sky Sports News.
"It's really special for an Englishman to be captain of PSG - especially on a night that meant so much to the club and the players. It was an amazing gesture and one I'll always be thankful for."