French champions PSG enjoyed most of the possession but took an over-cautious approach and injury-hit Real had the best chances through Cristiano Ronaldo and Jese in the first half.
The Spanish 10-times European champions stayed top of the group with seven points from three games and lead PSG on goal difference, with the reverse fixture to come in Madrid in two weeks time.
Malmo are third on three points after beating pointless Shakhtar Donetsk 1-0.
"We were in control and we had more opportunities than them. I do not care about possession, I care about how the team play," Real coach Rafael Benitez told a news conference.
Real entered the game having conceded only two goals in eight La Liga games and none in two matches in Europe and they looked solid throughout.
They were without the injured Gareth Bale, Karim Benzema and James Rodriguez.
PSG were almost at full strength with their preferred midfield of Blaise Matuidi, Thiago Motta and Marco Verratti, missing only centre back David Luiz through injury.
The hosts imposed their usual possession pattern on the game and had their first clear chance after 11 minutes when Matuidi's low shot was blocked by Keylor Navas.
Motta anchored the midfield as PSG played neatly although they were too slow up front and Angel Di Maria looked clumsy while striker Zlatan Ibrahimovic had a night to forget.
In true Benitez style, Real played tight, looking to bring the ball forward as quickly as possible when they had the chance, but PSG were vigilant.
The visitors had a big opportunity in the 25th minute when Kevin Trapp made a fine save from Jese after he had collected a brilliant through ball from Toni Kroos.
The German keeper was at it again 10 minutes from the interval, tipping Ronaldo's header over the bar as Real began to take control. Casemiro forced Trapp into another save with a long-range shot.
PSG were back in possession after the break and Edinson Cavani went close when he latched on to a cross from Motta in the 49th.
Lucas came on for Cavani and Di Maria made way for Javier Pastore as Laurent Blanc looked to spice it up up front shortly before Isco was replaced by Luka Modric for Real Madrid.
At the end of a sharp counter-attack, Ronaldo missed the target with a powerful angled shot.
(Editing by Ed Osmond)
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