The win was just their second ever at the famed venue.

Real are facing growing scrutiny under Xabi Alonso after managing just three wins from eight matches since early November, but struck first through Rodrygo.

The Brazilian ended a 33-game drought when he burst past O'Reilly on the right and drilled a low effort across Gianluigi Donnarumma. It was a deserved opener for the hosts, but their advantage did not last long.

City equalised when Thibaut Courtois pushed Josko Gvardiol's header straight into the path of O'Reilly, who finished from close range. Moments later, the visitors were handed a penalty after Antonio Rudiger bundled Erling Haaland over in the box and the striker converted confidently.

The hosts had the entire second half to try and find a way back into the match, with Vinicius Junior coming closest to getting his side back into the game, but it wasn't to be.

The win lifts City up to fourth in the league-phase standings. Real, meanwhile, slip to seventh and must now face Benfica and Monaco as pressure intensifies on Alonso.

After the match, Haaland told TNT Sports: "It's difficult to come here and the game has loads of transitions. We could have had another goal. I was close on one in the second half, Jeremy [Doku] was close a few times but the game was a bit chaotic. We can't really control it, which is difficult and it's difficult to come here, so in the end, we're super happy.

"It could have looked completely different today if we didn't win because we lost against Leverkusen, so this win is really important.

"Now we've got two more games left so we need to finish strong now and hopefully we can be in the first eight because then we're through."

Pep Guardiola acknowledged both the importance of the result and the room for improvement.

“Winning here, I have to be happy, especially in terms of points,” he said. "We have 13 already, so it's in our hands to finish in the top eight. That is the target. Winning here, after what happened against Leverkusen, has been good.

"Rodrygo, what a player. Vinicius, Bellingham and the pace they have up front is so dangerous and that's why you cannot stay high. You have to be so committed in the way you have to defend. We lacked a little bit, but in general, the effort was extraordinary.

"We are (far) away. Still, we are not ready (to win the Champions League). In February, we will be better. We have been here in the past, playing much than today, and we have lost. That's football sometimes.

"The players made an incredible effort, it was an incredibly good result, the spirit is unbelievable, but there are still margins to improve."

Alonso, whose position is under mounting threat, maintained that his players gave everything despite another setback.

“The performance has been intense. A professional Champions League level game. They have given their best, so from my side no complaints for anything,” he said.

"It is hard to take another defeat but we tried until the end."

Man City rally to beat Real Madrid at Bernabeu as pressure mounts on Xabi Alonso