Carlo Ancelotti's side have not made the last eight of Europe's elite competition for 18 years, but they made no mistakes in the second leg after taking a 2-1 lead into the match after the first clash in Spain last month.
Jonas had given Valencia some hope when he opened the scoring on the night, ten minutes into the second half, but it was not to be for the two-time finalists as PSG levelled through Ezequiel Lavezzi on 66 minutes.
PSG had gone into the game without their two biggest names in Zlatan Ibrahimovic and David Beckham, with the Swede suspended and the Englishman on the bench - but they started brightly with their South American attacking triumvirate of Lavezzi, Lucas Moura and Javier Pastore seeing plenty of the ball.
Indeed the first chance came through Lucas as a delicious flick took him past Jeremy Mathieu and in on goal, but he dragged his shot wide.
PSG, though, seemed happy to sit back with their aggregate lead in the bag from the first leg and allowed Valencia to come into the game.
The first shot on target came via Roberto Soldado 15 minutes in as he linked up brilliantly with strike-partner Jonas, playing a one-two with the Brazilian before striking at goal, but it was straight at Salvatore Sirigu.
Indeed Sirigu was the busier keeper, as Vicente Guaita, save for a couple of punched clearances from set-pieces, was untested in the opening 45 minutes.
Just before the break Sirigu did well to parry a Jonas shot which his defence cleared behind. The resulting corner saw Pastore head the ball just wide of his own goal as Valencia finished the half brightly.
The Spanish outfit began the second period as they finished the first, on top and they introduced Ever Banega to add some extra attacking impetus from midfield.
It was not long before they went ahead on the night and it was a brilliant strike. Blaise Matuidi was dispossessed in midfield and the ball fell for Jonas who thundered the ball past Sirigu from 25 yards.
Ancelotti responded to going a goal down by bringing on Kevin Gameiro, and the one-time Newcastle United target made a huge difference with a number of probing runs.
And Gameiro was at the heart of the equaliser which came just after the hour. He drove for goal and worked his way clear before the ball bounced into the path of Lavezzi, who saw his first shot brilliantly saved by Guaita but he put the rebound away off his thigh and sealed PSG's passage into the last eight.