The hosts dominated possession in the game's early moments, but it was Newcastle who took the lead against the run of play on 18 minutes as Aleksandar Mitrovic met Georginio Wijnaldum's cross with a header.
The visitors thought they had doubled their lead on 25 minutes as Mitrovic tapped in at the near post, but the goal was ruled out for offside, before the Serbian tested Hart with a fierce strike in the box.
After the break the Citizens wasted no time in asserting control on the rest of the match, as Aguero netted for the second time on 49 minutes after Silva played the striker in on the left of the penalty area.
Aguero wrapped up his hat-trick just a minute later, as Kevin De Bruyne found the Argentine one-on-one with Krul before the striker lofted the ball over the Dutch goalkeeper and into the back of the net.
City scored their fourth goal on 54 minutes as Kevin De Bruyne struck a right-footed looping volley beyond Krul from the near post.
With the visitors completely rocked, City added another goal on 60 minutes as Silva found Aguero, who dropped the shoulder before firing into the Newcastle goal.
Just two minutes later, the Argentine added his fifth goal of the afternoon as De Bruyne sent a low cross into the Newcastle penalty area, before Aguero tapped in.
The match calmed down after Aguero was replaced by Wilfried Bony, but the hosts continued to dominate as the Ivorian fired wide from an Aleksandar Kolarov cross, before Kelechi Iheanacho forced a good save from Krul.