PSG reached the last eight for the first time in 18 years, squeezing past Valencia 3-2 on aggregate with a 1-1 home draw on Wednesday having only for about 10 minutes looked in danger of being knocked out.
Valencia went 1-0 up courtesy of Jonas's strike in the 55th minute but Ezequiel Lavezzi equalised in the 66th minute.
The club has spent 200 million euros on transfers since Qatar investors took over in 2011 so expectation is high, but despite their place in the last eight, PSG have yet to be really tested.
They played Porto, Dynamo Kiev and Dinamo Zagreb in their group games, winning five of the six matches. The defeat was a 1-0 loss at Porto.
"I do not know if we can go all the way," said coach Carlo Ancelotti, who took over from Antoine Kombouare in Dec. 2011.
"At the beginning of the competition, nobody knew what we could do. Reaching the quarter-finals on the first year is something fantastic."
PSG's undeniable qualities are offset by worrying shortcomings when it comes to inspiration.
They rely on a backbone of goalkeeper Salvatore Sirigu, centre back Thiago Silva, midfielder Blaise Matuidi and striker Zlatan Ibrahimovic.
Sirigu has been solid since joining from Palermo in 2011, former AC Milan defender Thiago has shown stunning composure and France international Matuidi is, according to Ancelotti, "one of the best midfielders in Europe".
Ibrahimovic has netted 22 goals from 24 games in Ligue 1 but was suspended on Wednesday and his creative spirit was sorely missed as PSG looked short of ideas up front despite Javier Pastore's efforts.
As usual, PSG surrendered possession, with Valencia enjoying almost 65 per cent of it, a statistic they would expect to pay dearly for against the likes of Real Madrid, Juventus or Barcelona should they qualify.
"We experienced several problems during this game," midfielder Clement Chantome conceded.
"We did not play a great game but the most important thing was to qualify for the quarter-finals," said striker Kevin Gameiro, whose dazzling run led to Lavezzi's equaliser.
The draw will be made on March 15 and PSG could get a favourable tie against the likes of Schalke 04, Galatasaray or Malaga.
"We know that if we want to play the final, we will have to beat big teams anyway," said Chantome.