Pep Guardiola says the football world will "kill" Manchester City if they fail to impress in Tuesday's Champions League round-of-16 first-leg tie against Monaco.
But again Monaco responded, with Falcao making a fool of Stones in the area and chipping Caballero for a delightful goal.
Early in the second half, Nicolas Otamendi's challenge on Falcao gave the French side a odd penalty but Willy Caballero saved his weak spot-kick to keep the score 2-1.
Stay tuned here for highlights of goals and key plays throughout the match. Attention will focus on City's top scorer Sergio Aguero, who is back leading the line following an injury to impressive new signing Gabriel Jesus.
Kamil Glik, whose early booking ensured he will miss the second leg, headed narrowly wide amid a high-tempo start that set the tone for an enthralling contest.
Forward Kevin De Bruyne said: "This team is building on that but we need time to do that year after year". The two strikers are fighters - [Radamel] Falcao and [Valere] Germain, they are killers in the box.
Radamel Falcao would however equalize with a diving header from Fabinho's cross.
It was City, though, who went in front in the 26th minute. Put clear on the goalkeeper down the right channel, he powerfully sidefooted into the near top corner to leave Caballero grasping at air and Monaco dreaming of the quarter-final.
After a good 10 or 15 seconds and to the disbelief of the home support, he pointed to the spot.
Yet there may have been an element of justice done when Falcao's low and soft penalty was easily saved after the Colombian's stuttered run-up did nothing to fool Caballero.
On the other hand, Monaco boss Jardim said: "They are strong in the transition, they have five forwards at some point when they pour forward".
Sterling won the ball inside his own half and charged down the pitch, releasing Aguero with a lovely pass. His effort took a bobble, however, and crept in over the red-faced keeper's left foot. He picked up the ball, chased back, and with their next attack City had an implausible lead, for the first time since six goals ago.
The visitors managed to take the lead just before the break as Kylian Mbappé latched onto a long ball, before rifling the ball past Willy Caballero.
"I am happy for him, he is a good professional and a nice guy".
Three minutes later, City supporters protested heavily.
Any pretence of a controlled tactical battle was lost soon after as City added a fifth.
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