Los Blancos had won the first-leg 3-1 at the Santiago Bernabeu a fortnight ago.
The first chance of the game this week fell to Sergio Ramos in the 19th minute and the defender almost found the opener for Zinedine Zidane's charges with a strike at the near post, but goalkeeper Alphonse Areola produced a brilliant reflex save.
PSG were starting to boss the game after 25 minutes and found openings in the last third, although they were largely limited to taking shots from distance, none of which troubled shot-stopper Keylor Navas.
Angel Di Maria, who started in place of the injured Neymar, was particularly threatening up front for Unai Emery's troops but his synergy with the attacking players was not yet clicking.
Karim Benzema should have broken the deadlock for the visitors seven minutes before the break after beating the offside trap to go one-on-one with PSG goalkeeper Areola, but the French shot-stopper narrowed the angle and made a great save to deny his compatriot.
Five minutes into the second half, Cristiano Ronaldo put the visitors ahead by converting Lucas Vazquez's cross at the far post with a downward header.
Things went from bad to worse for the Parisians in the 65th minute after Marco Verratti received his second booking for dissent. The home side had to play the last 25 minutes with a man down and three goals behind.
Edinson Cavani gave PSG hope in the 71st minute rather fortuitously after Javier Pastore's diving header inside the box went through a couple of Madrid players inside before hitting the Uruguayan last and trickling into the net.
However, Casemiro crashed hopes of a comeback for PSG with 10 minutes left with a deflected effort from the edge of the box.