Adrien Rabiot opened the scoring for the French league leaders in the 33rd minute at the Santiago Bernabeu on Wednesday night. But on the stroke of half-time Cristiano Ronaldo levelled for the hosts from the penalty spot.
It was the Portugal international's 100th goal in the Champions League and the 32-year-old increased his tally seven minutes from time. Marcelo added the gloss in the 86th minute.
Despite the disappointment, PSG striker Neymar insisted that his side could still advance to the last eight. The 25-year-old Brazilian was in the Barcelona side that lost 4-0 at PSG in the first leg of the last 16 last season. The Catalans won the return leg 6-1 to progress 6-5 on aggregate.
"I think it will be difficult but nothing is impossible," said Neymar of the return leg on 6 March at the Parc des Princes.
"Last year with Barcelona I was in a much worse situation and we managed to get through. I hope we will be able to play better."
Nasser Al-Khelaifi, the PSG president, said: "We have to think about the next match and the next 90 minutes. It really isn't over. We'll have our supporters and Real will find it difficult. I know our players will give 200 per cent to qualify."
PSG midfielder Marco Verratti added: "We can't go out in the last 16 again. We'll be ready for the secon dleg as it will be a crucial match for us. None of us will hid on the pitch."
The victory eased the pressure on Madrid boss Zinedine Zidane. His men have virtually waved goodbye to their La Liga crown. The Spanish champions lie fourth 17 points adrift of Barcleona with 16 games to play.
"We can be happy with the way we played," said Zidane who has steered Madrid to consecutive Champions League titles. "We kept going to the end. It is a good result and the team deserve to be congratulated.
"It was a good evening, we completely deserved our victory. Everything was good and everyone played an important role."
In contrast, the PSG coach, Unai Emery, focused his frustration on the Italian referee Gianluca Rocchi.
"The team played well. They showed character. We deserved a better result but the referee did not help us," said Emery. "Their penalty was not very clear and there was a clear penalty for us for a handball by Sergio Ramos," he said. "The referee took decisions that damaged us."