Teammate Vincent Kompany hailed Sergio Aguero as Manchester City's "special player" after the Argentine's hat-trick earned a rousing 3-2 comeback win over Bayern Munich in the Champions League on Tuesday.

The victory resuscitated City's hopes of qualifying for the last 16 ahead of its final Group E match against AS Roma.

Should the Premier League champion win in Rome on Dec 10 and CSKA Moscow fails to beat Bayern, Manuel Pellegrini's team will go through.

Aguero struck twice late on with clinical, unerring finishes having earlier given the host the lead with a first-half penalty.

Before his timely intervention Bayern seemed ready to send City's campaign plunging to a new low as its 10 men led 2-1 with five minutes remaining.

"If you want to succeed at anything you need to have a special player in special form," Belgium defender Kompany told ITV Sport. "Sergio Aguero is our special player and when he is in that form he makes things achievable.

"It was an awkward game. They were incredibly lethal and played well with 10 men but we did what we had to do and defeated a big team."

Kompany said the squad is looking forward to Dec 10.

"What a game it will be against Roma," he said. "We will take a lot of fans and the atmosphere will be incredible."

Pellegrini echoed his captain's sentiments and praised City's determination.

"I think all the big teams need big players, Sergio Aguero is a big player and very important," said the manager.

"The whole team played until the end, we conceded two unbelievable goals but our whole team kept working and concentrating."

The Chilean was coy when asked if City's stunning late rally against the 2013 Champions League winner could prompt an upturn in its European fortunes.

"We'll see ... but we have to play another game. We had the obligation to win our two games and we have won our first one," said Pellegrini.

"We know we don't depend on only what we can do because if CSKA win in Germany they qualify for the next round but we have to do our duty and our duty is to beat Roma."

Bayern fell to its first loss in 19 competitive games this season, losing focus late on having played a man short from the 20th minute when Benatia - as last man - fouled Aguero as the striker prepared to shoot. The centerback was given a straight red card.

Bayern toyed with City in a 3-1 win here in last season's group stage and it was the same 13 months later. With Alonso - on his 33rd birthday - running the game from the base of Bayern's midfield, it was hard to know which team was a player short at times.

"We gave them the game," Bayern coach Pep Guardiola said. "They had hardly any chances with 11 against 10 ... we were tired in the last 10 minutes."