After a period of sustained pressure, the breakthrough came after half an hour, when Walker’s clever low cross from the right evaded everyone and nestled into the bottom corner of the net.
A strong start to the second half was essential if City wanted to assert their dominance on the game, and they achieved just that.
And Jesus added a third soon after, plucking Bernardo Silva’s header back across goal exquisitely out of the air before smashing past Freddie Woodman.
The hosts hit back through a smart turn and finish from Morgan Whittaker in the 77th minute, but the damage had already been done, and City held out for a 15th consecutive victory in all competitions.
Pep Guardiola's men will find out who they face in the last eight on Thursday evening, following the final tie of Round Five between Barnsley and Chelsea.
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