Los Blancos would have been looking to start their Group A campaign with a positive result at the Parc des Princes, but PSG had other ideas as they collected all three points with an impressive victory on home soil.
Di Maria scored twice in the first period for the Ligue 1 champions before Thomas Meunier added a third in second-half stoppage time on a tough night for Zinedine Zidane's side, who had two goals disallowed.
PSG were without the services of Neymar through suspension, while Kylian Mbappe and Edinson Cavani were also absent through injury, meaning that summer arrival Mauro Icardi led the French side's line.
After a fairly slow start to proceedings, PSG made the breakthrough in the 13th minute when Juan Bernat's low cross was poked into the back of the net by Di Maria.
The Argentina international's effort came quickly at Thibaut Courtois, but the Madrid stopper will surely have felt that he should have done more in an attempt to prevent the ball from flying past him.
Hazard looked to answer back shortly after as the Belgian found space in a dangerous position before attempting to pick out the bottom corner, but the ball just flew wide of Keylor Navas's post.
James Rodriguez then fired high and wide before Benzema headed a Bale cross past the post as the visitors looked to respond inside the first 25 minutes in the French capital.
Zidane's side had another opportunity in the 32nd minute from a free kick in a dangerous position, but Bale saw his effort just dip over Navas's crossbar at the final moment.
PSG doubled their lead moments later, with the impressive Di Maria picking out the corner from distance after being found by Idrissa Gueye in a dangerous position.
Madrid thought that they were back in the match two minutes later as Bale managed to lift the ball over the PSG goalkeeper with a clever finish from distance. However, the goal was disallowed by referee Anthony Taylor for handball following a VAR check, much to the delight of the home supporters.
The French champions might have scored a third in the latter stages of the half when Icardi spun inside the Madrid box before looking to find the back of the net, but Courtois was on hand to make a comfortable save.
Bale then struck a powerful attempt just wide of the post down the other end as PSG's two-goal lead stood at the interval, leaving Zidane with much to ponder ahead of the second period.
The visitors had plenty of possession in the early stages of the second half; the majority of the threat was coming from PSG, though, with the French champions looking to put the game beyond their opponents.
Di Maria had a golden chance to complete his hat-trick just before the hour after breaking into the Madrid box, but the Argentina international scooped his effort over the crossbar.
The South American then turned provider for the tricky Pablo Sarabia, who saw his close-range effort saved by Courtois with Zidane's side on the ropes as they continued to come under pressure.
Hazard was doing his best to make things happen for Madrid; it was not the Belgium international's night, though, as he remained off the pace before being replaced in the 70th minute by Lucas Vazquez.
Luka Jovic was also introduced off the Madrid bench, and the capital giants again had the ball in the back of the PSG net in the 77th minute through Benzema, only for the flag to be raised for offside.
Benzema then headed just wide of the PSG goal in the 79th minute before Vinicius Junior replaced Bale in Madrid's third and final change. It was not to be for the away team, though, and they conceded a third in stoppage time when Meunier scored from close range after combining with fellow full-back Bernat.
Los Blancos will attempt to return to winning ways when they travel to table-topping Sevilla in La Liga on Sunday, while PSG are next in Ligue 1 action away to Lyon on the same night.
PARIS SAINT-GERMAIN (4-3-3): Navas; Meunier, Silva, Kimpembe, Bernat; Verratti, Gueye, Marquinhos (Herrera 70'); Di Maria, Icardi (Choupo-Moting 60'), Sarabia (Diallo 89')
REAL MADRID (4-3-3): Courtois; Carvajal, Varane, Militao, Mendy; Kroos, Casemiro, James (Jovic 70'); Hazard (Lucas 70'), Benzema, Bale (Vinicius 79')