The second half followed the same pattern, with City repeatedly on the attack and any hopes Newcastle had of earning a point seemed to evaporate when Manquillo hauled down Sterling in the 63rd minute.
Aguero blasted the ensuing penalty past Darlow to double City’s advantage.
Yet, almost immediately, City were caught napping at the back and Murphy raced through on goal and lifted the ball over Ederson to halve the deficit.
Newcastle’s spirits were raised further by Darlow’s extraordinary reflex save from Sterling and, all of a sudden, the Magpies were revitalised as Mohamed Diame twice tested Ederson from close range.
However, with seven minutes remaining, City secured the three points — and settled their nerves — when Sane went on a mazy 30-yard run that sucked in most of Newcastle’s defence before he squared into the middle of the box where Aguero calmly completed his latest treble.