Barcelona's poor start to 2017 continued as they lost further ground on Real Madrid at the top of La Liga despite a sensational last minute Lionel Messi free-kick salvaging a 1-1 draw at Villarreal on Sunday.
The Spanish champions lost their opening game of the year at Athletic Bilbao in the Copa del Rey on Thursday and now trail Real by five points having also played a game more.
Italian forward Nicola Sansone looked to have handed Villarreal a first win over Barca since 2008, but Messi's late intervention denied the hosts on the day they announced a sponsorship deal to rename El Madrigal the Ceramic Stadium.
A draw leaves Villarreal still in fifth, a point adrift of Atletico Madrid in the final Champions League place.
"It can't be a positive analysis of the game because we needed the three points and I think we did enough to deserve the three points," Barca boss Luis Enrique told Spanish TV station Movistar.
However, Enrique insisted Barca remain very much in the title hunt despite their chances now depending on a Madrid collapse in the second half of the season.
"There is still half the season to go and I am sure we will have the chance to fight for the league," he added.
"The only chance we will have to fight for the title, though, is by getting back to winning soon. To keep playing like this but with a different result."
Barca dominated possession throughout, but struggled to create clear-cut chances against the tightest defence in La Liga.
Indeed it was the hosts who enjoyed the best opportunity of the opening half when former Barca midfielder Jonathan dos Santos blasted over when unmarked at the back post from a flowing counter-attack.
Messi came close in unusual fashion as his thumping header from a corner was tipped over by Sergio Asenjo before Luis Suarez's fiercely hit drive was also too close to the Villarreal 'keeper.
Another Villarreal counter-attack caught the Spanish champions cold at the start of the second-half as Alexandre Pato's perfectly weighted pass picked out Sansone and his effort back across goal nestled in the far corner.
Barca had a fine chance to immediately respond when a quickly taken Messi free-kick freed Neymar inside the area, but again the Brazilian's effort lacked the power or accuracy to unduly trouble Asenjo.
The visitors had huge claims for a penalty waved away when Villarreal captain Bruno deflected Messi's effort over with an outstretched hand and seconds later Messi smashed the inside the post with a fine effort from the edge of the box.
The controversial penalty calls were evened up as referee Ignacio Iglesias Villanueva was also unmoved when Sansone's shot struck Javier Mascherano's hand inside the Barca box.
And Messi finally broke Villarreal's resistence as he was fouled on th edge of the area and stepped up to arrow a free-kick perfectly into the top corner.
Villarreal ended with 10 men as Jaume Costa saw a second yellow card deep into stoppage time, but there was barely time to restart the game before blew for full-time and arguably brought the curtain down on Barca's title defence.
Elsewhere, Celta Vigo moved into the top half of the table as Iago Aspas moved level with Cristiano Ronaldo on 11 La Liga goals for the season in a 3-1 win over Malaga.
Athletic Bilbao remain seventh after being held 0-0 in a Basque derby at home to Alaves.
And Real Betis moved nine points clear of the relegation zone thanks to a 2-0 win over fellow strugglers Leganes.
However, Neymar restored Barca's belief as he firstly fired home a sensational free-kick two minutes from time and then converted from the penalty spot.
And substitute midfielder Roberto became the unlikely hero when he stretched to turn home Neymar's sublime chip over the defence, leaving the score 6-5 on aggregate as the crowd dissolved into ecstasy.
"I threw myself at it with everything," Roberto told BeIN Sports. "We left Paris very down and now this is incredible.
"We were prepared for all this. The fans were like 10 extra players and in the end this is all for them."
Midfielder Ivan Rakitic said Barca had defied the critics after their first-leg humiliation in Paris three weeks ago.
"It's crazy. After Paris, many people spoke hard about our team but tonight was special, we made history," the Croatian told BT Sport.
"We know we are the best team in the world."
As well as staying on course for a sixth title, the 1992, 2006, 2009, 2011 and 2015 European champions set a new record by reaching their 10th straight quarter-final.
PSG coach Emery admitted his team went to pieces in the final minutes, but said they were badly affected by the two second-half penalties given by German referee Deniz Aytekin.
"In the second-half it changed. The (Messi) penalty got them off to a great start, but I was already calmer because I could see the team was responding better, were better positioned on the pitch and could do damage," said the Spanish coach.
"We had chances to make it 3-2 and then the refereeing decisions, I don't know if they were right or not, but for sure they damaged us. Then in the last two minutes we lost everything we had recovered in the second-half."
Barcelona defender Gerard Pique, husband of Colombian pop star Shakira, predicted exuberant celebrations among the team's fans.
"I would say to the hospitals of Barcelona to hire nurses," said the father of two. "Tonight people will make a lot of love.
