The reigning European champions entered the match with a 3-1 advantage from the first leg at the Bernabeu, and finished the job in the French capital to march into the last eight.
The absence of Neymar meant that Angel Di Maria started alongside Edinson Cavani and Kylian Mbappe in the PSG attack, while Thiago Silva and Thiago Motta were both recalled following the first leg in Madrid.
As for Real Madrid, Luka Modric and Toni Kroos were only fit enough for the bench. Mateo Kovacic started alongside Casemiro in midfield, while Marco Asensio and Lucas Vazquez were also handed spots in the XI. Gareth Bale was fit and available, but the Welshman was among the substitutes for the visitors.
A frantic opening 10 minutes saw both teams concede possession on a number of occasions, but PSG - and in particular Di Maria - were making things happen in forward areas.
It was Real Madrid that had the first half-chance of the match in the 11th minute, but Karim Benzema saw his effort from the edge of the box deflected over the crossbar.
Di Maria had a long-range free kick deflected over the Real Madrid crossbar in the 26th minute as PSG looked to strike first, but the home side were finding it difficult to create clear opportunities.
Benzema had a wonderful chance to send the visitors ahead when he broke into the PSG box seven minutes before the interval, but the Frenchman's low strike was kept out by Areola.
Di Maria then brought a smart save from Keylor Navas down the other end, before the Real Madrid goalkeeper kept out Mbappe's low strike in the 43rd minute as the two teams headed down the tunnel at 0-0.
Ronaldo made no mistake one minute later, however, with the attacker hanging in the air at the far post to head a Vazquez cross into the back of the home side's net.
PSG were then reduced to 10 men in the 66th minute when Marco Verratti picked up his second yellow card for dissent, which left the hosts with a mountain to climb in Paris.
Asensio came close to sending Real Madrid 2-0 ahead 20 minutes from time after meeting a low cross from Benzema, only for his effort to strike the post.
PSG registered in the 71st minute when Pastore's header hit Casemiro before deflecting onto Cavani and in, which left the Ligue 1 leaders needing two goals in the latter stages to force extra time.
Benzema saw one deflected just wide of the PSG post in the 75th minute as Real Madrid continued to create chances, and the visitors had their second 10 minutes from time when Casemiro saw his effort deflected into the corner of the net.
Vazquez struck the post in the 83d minute as the Spanish side looked for more goals, before Isco brought a smart save from Areola in the 90th minute as Real Madrid, who have become the first team to win at Parc des Princes this season, showed their dominance to ease into the quarter-finals.
PSG (4-3-3): Areola; Alves, Silva, Marquinhos, Berchiche; Rabiot, Verratti, Motta (Pastore 59'); Mbappe (Diarra 85'), Cavani, Di Maria (Draxler 76')
REAL MADRID (4-4-2): Navas; Carvajal, Varane, Ramos, Marcelo; Lucas, Casemiro, Kovacic (Kroos 71'), Asensio (Isco 82'); Benzema (Bale 76'), Ronaldo