Aleksandar Mitrovic nodded Newcastle in front but Aguero's brilliant burst of goals began when he headed City level.
It continued after the break when his deflected shot made it 2-1 and he ran through soon after for his hat-trick.
Kevin de Bruyne's volley made it 4-1 before Aguero struck again with a curling shot and close-range finish.
Newcastle, who are still without a league win this season, had chances to extend their lead after seeing £13m striker Mitrovic score his first goal since joining the club in the summer.
But Aguero's virtuoso show means the Magpies fall to the bottom of the table on goal difference as he ended his Premier League goal drought in style.
Source: BBC Sport
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