The LaLiga side was the better team but the Premier League champions remain in the tie thanks to second-half goal from Jamie Vardy.
The first competitive meeting between Manchester City and Monaco will live long in the memory as the sides shared eight goals.
The Brazilian attacker came off the bench with 15 minutes to go but gave the Nerazzurri the lead to ensure they stay in the European spots in Serie A.
The Gabon international spurned numerous chances and saw his limp penalty saved by Ederson before being taken off after an hour.
Robert Lewandowski was guilty of missing the best chances for the visitors, who still got all three points with the late heroics of his team-mates.
The Bianconeri extended their lead over Roma in Serie A to four points and have a game in hand over the second-place side.
The defender has been linked with a move away from Stamford Bridge, but got himself on the scoresheet along with Willian, Pedro and Michy Batshuayi.
Richard Stearman and Andreas Weimann got the goals for the visitors, with a reply from Divock Origi unable to shake the Reds from their 2017 struggles.