PSG, with David Beckham left on the bench, drew 1-1 at home to Spanish side Valencia at the Parc des Princes which allowed them to progress 3-2 on aggregate.
They had to survive something of a scare, however, with Brazilian attacking midfielder Jonas putting the visitors in front on the night 10 minutes into the second half.
But PSG settled their nerves when Ezequiel Lavezzi, who had also scored at the Mestalla in the first leg, levelled in the 66th minute and PSG held out to secure their place in the last eight for the first time since 1995.
In Turin, Juventus, the champions in 1985 and 1996, cruised into the quarter-finals with a 2-0 win over Celtic for an impressive 5-0 aggregate scoreline.
Strikes in either half from Alessandro Matri and Fabio Quaglirella earned Juventus the win, ending all hopes of the "minor miracle" which Celtic manager Neil Lennon had deemed necessary on the eve of the tie.
"It may have looked easy, but if we had conceded a goal, then you know how things can turn around, you start to worry," said Matri.
"But we scored a good goal and I am happy to have got the goal."
Lennon accepted that the Italian challenge was a step too far but praised his side for a memorable campaign which had included a famous group stage win over Barcelona.
"On the night, was it a fair result? Class tells in the end," said Lennon.
Juve were ahead after 24 minutes when Federico Peluso robbed Celtic striker Gary Hooper and fed Quagliarella to the left of goal.
When Fraser Forster failed to hold the Italian's shot, Matri ran in to sweep the ball home.
Lennon replaced right-back Adam Matthews with Efe Ambrose -- blamed for two of Juve's first leg goals -- at half-time, but it was Juve who moved up a gear.
When Juve's second goal came, it exposed Celtic's defence all too easily.
A long ball from midfield was flighted in for Arturo Vidal, who sneaked in behind Emilio Izaguirre to collect and square for the unmarked Quagliarella to slot home past Forster at the back post.
Meanwhile, Manchester United manager Alex Ferguson and his players face disciplinary action after refusing to speak to the media following their controversial Champions League exit to Real Madrid.
Ferguson is in trouble for not attending the mandatory press conference after his side's 2-1 loss to Real at Old Trafford, a game which turned on the second-half dismissal of Nani.
Assistant manager Mike Phelan faced the press instead while United players passed through the mixed zone refusing to talk to reporters following the team's 3-2 aggregate exit.
The last-16 stage will be completed next week when Schalke and Galatasaray resume after their first leg ended 1-1 and AC Milan take a 2-0 lead to Barcelona.
FC Porto carry a 1-0 advantage to Malaga while Arsenal will try and keep British hopes alive by overturning a 3-1 deficit at Bayern Munich.