Manchester United fought back from two goals down to beat Roma 3-2 in the Champions League on Tuesday to hand beleaguered manager Michael Carrick a reprieve, while holders Paris Saint-Germain continued their perfect start in the competition by hitting Villarreal for six.

Looking set for another abject defeat when two behind within 18 minutes through a smart Mathias Soule finish and Donyell Malen's penalty, United staged a thrilling comeback in the second half to turn a poisonous atmosphere at Old Trafford to one of joy.

Matheus Cunha, who was sent off in stoppage time, saved the day for United with a brace in three minutes with the final whistle nearing, sparking wild celebrations in the stands.

Those scenes at the end of the game couldn't have been more different to the anger which pulsated around the ground in the first half, when United fans threw tennis balls and other objects onto the Old Trafford pitch and directed foul-mouthed chants at the club's majority owners, the Glazer family.

"We knew that the fans would be behind us until the last day, we just had to get a result for them," United captain Bruno Fernandes told TNT.

United head into Sunday's match with Aston Villa, beaten 3-0 at Barcelona, in an entirely different mood after punishing slapdash Roma who vanished in the second half after having shown why they look like league title contenders in Italy.

"I spoke at half-time about being positive. Anything can happen here, I've seen it many times over the years," said Carrick.

"You just need something to go our way and the boys were fantastic second half."

Roma, who also threw away a commanding lead to lose to Real Madrid, failed to deal a knockout blow and crumbled once Bruno Fernandes pulled United back into the game in the 58th minute at the second time of asking from the penalty spot.

The Portuguese thumped home past Roma's third-choice goalkeeper Devis Vasquez, who saved the first attempt but was let down by his teammates encroaching in the penalty area.

And that set up Cunha to hit Roma with a one-two that decided a thrilling encounter and gave Carrick some breathing room with the international break coming up after the weekend.

PERFECT PSG 

PSG were in ruthless mood even without star player Khvicha Kvaratskhelia as they put Villarreal to the sword on a night in which Europe's elite clubs paid tribute to tragic Tenerife player Jesus de Miguel with a moment's silence before kick-offs.

De Miguel died aged 30 from injuries he suffered in a sickening collision with FC Andorra's goalkeeper in a Spanish second-division match, leaving football in mourning and condolences pouring in from around the globe.

PSG tore into sorry Villarreal, with Joao Neves, Desire Doue, Senny Mayulu and Fabian Ruiz all striking in eight first-half minutes as the French outfit set a record for the fastest four goals scored in a match in Europe's elite club competition.

It certainly didn't look like PSG were missing Kvaratskhelia, Ousmane Dembele, captain Marquinhos and Nuno Mendes, and further strikes from Spain World Cup star Ruiz and teenager David Boly rounded off a stellar performance which put Luis Enrique's team top of the table.

"We were impressive throughout and we are really pleased even if it is very difficult for Villarreal," said Luis Enrique.

"But it is hard when you play against a team like us that presses constantly."

Another team missing a host of stars in Bayern Munich saw off Atletico 2-0 to move into the top eight positions.

Teenage Germany forward Lennart Karl and Konrad Laimer netted in the second half in Madrid as Bayern triumphed despite a bulging casualty ward.

Jamal Musiala, Luis Diaz, Serge Gnabry and Ismael Saibari were on Bayern's injury list but it meant little as freshly-minted Ballon d'Or winner Harry Kane and captain Joshua Kimmich marshalled his troops to a memorable victory.

Inter Milan recovered from derby defeat at the weekend with a comfortable 3-0 win over Feyenoord which came through goals from Yann Bisseck, Pio Esposito and Piotr Zielinski.

Raphinha, meanwhile, struck twice to propel Barcelona to a 3-0 win over visitors Aston Villa, ending the English side's perfect start to the competition.

Five-time winners Barcelona took an early lead through Lamine Yamal before Raphinha continued his fine goalscoring form with a second-half brace.