Pep Guardiola's side began the encounter on the front foot, pressing the hosts high up the pitch and earning multiple corner kicks to pile on the pressure.
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Chelsea struggled to contain the free-flowing City, but it wasn't until eight minutes after the interval that the deadlock was broken - as Jesus expertly turned and fired into the bottom corner via a deflection from 15 yards.
City weren't content to sit on the one goal lead and almost doubled the lead through Jesus again, but his rolled effort was expertly cleared off the line by his compatriot Thiago Silva.
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More chances came and went for City - the most clear one falling at the feet of Jack Grealish, who raced through on goal but was denied well by Edouard Mendy.
Guardiola's men, led my Ruben Dias, remained resolute to claim all three points in London!
See the best pictures from the encounter via the gallery below.